MAT331, Feb 25th, 2010 If a curve fits, wear it (Chapter 2 of the online book) restart; pts:=[[9.461625032, -15.00000412], [-4.026835626, 5.229076781], [-8.417983819, 17.28331107], [7.335537549, -10.75702150], [.667622007, 1.352242696], [-3.642662167, 8.570158849], [4.108941669, -6.649973580], [-3.592756472, 7.661525316], [0.121773384e-1, -.5948721361], [3.588065808, -7.386147022], [9.371019578, -17.50451275], [6.303804064, -11.16461096], [9.396335873, -15.62444142], [-.807790200, 2.555503241], [.782176902, -4.501842488], [3.640727999, -6.449402329], [1.668897236, -3.014773741], [3.704029489, -3.221704164], [-11.29937335, 17.53901720], [8.475940602, -17.91640911], [-3.666884970, 8.440428354], [-5.617368657, 12.00375535], [-5.626834452, 7.337908700], [-2.138751424, 5.625807468], [-2.268585475, 4.613703098]]: with(plots): distancePointLine:=P->(m*P[1]+b-P[2])^2;

Zio2I0kiUEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiQsKComSSJtR0YlIiIiJjkkNiNGLUYtRi1JImJHRiVGLSZGLzYjIiIjISIiRjRGJUYlRiU=

distancePointsLine:=pts->sum(distancePointLine(pts[i]),i=1..nops(pts));

Zio2I0kkcHRzRzYiRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSRzdW1HRiU2JC1JMmRpc3RhbmNlUG9pbnRMaW5lR0YlNiMmOSQ2I0kiaUdGJS9GMjsiIiItSSVub3BzRyUqcHJvdGVjdGVkRzYjRjBGJUYlRiU=

DD:=distancePointsLine(pts): simplify(DD);

LC5JIm1HNiIkIisuei54RyEiJ0kiYkdGJCQiK1JhbDlWISIpKiRGIyIiIyQiK11MZyY+KSEiKComRiMiIiJGKEYyJCIrMlxAI1skRisqJEYoRi0kIiNEIiIhJCIrS0VrOEVGJ0Yy

eq1:=diff(DD,m); eq2:=diff(DD,b);

LChJIm1HNiIkIitwMTdSOyEiJ0kiYkdGJCQiKzRcQCNbJCEiKSQiKy16LnhHRiciIiI=

LChJIm1HNiIkIis0XEAjWyQhIilJImJHRiQiI10kIitPYWw5VkYnIiIi

plot3d(DD, m=-2..-1,b=-0.8..2,axes=boxed,style=patchcontour);

-%'PLOT3DG6(-%%GRIDG6%;$!#?!""$!#5!"";$!")!""$"2$**************>!#;7;7;$"1*Qv*4O1]<!#8$"2(*>>no&)en"!#9$"2kc=!>L^3;!#9$"2#)[to]Yza"!#9$"1mRG]_=%\"!#8$"2&***\#\&HsW"!#9$"2))erPSzqS"!#9$"2Kt[Q"[tt8!#9$"2FV"[zd>Z8!#9$"2))op1IiuK"!#9$"2%*\8uPMXJ"!#9$"2e'Gr4?T38!#9$"2&)ynv>&448!#9$"1m#y4%Re;8!#8$"2$*HW*R#y3L"!#9$"2#))eY%4y>N"!#9$"1LIa/N))z8!#8$"1Ld<qWf99!#8$"2)))RO"*46c9!#9$"/y5oIV/:!#6$"2k;2/qg&f:!#9$"2&)3i#))Q\@;!#9$"2mcs;jK-p"!#9$"2&*fQ1$pxl<!#9$"1)=g^yE"[=!#87;$"1x1A1m^&e"!#8$"1**>KE9.8:!#8$"2k()y>!=NZ9!#9$"2(48>LxZ)Q"!#9$"2')Hf*>#4kL"!#9$"1VGGii9"H"!#8$"2L%>;g))o_7!#9$"2))f'f8q.@7!#9$"2(4oeA2>'>"!#9$"2ldKr)*\"y6!#9$"2()*QB2["p;"!#9$"2ix!*G=&[i6!#9$"2'4K596'[;"!#9$"2))>r3gUS<"!#9$"2Ku%>V'H+>"!#9$"1VQ2TA#G@"!#8$"2')\3XR?CC"!#9$"2)4()\.T#)y7!#9$"2nZW!oL.A8!#9$"2))zX")=[?P"!#9$"2jn-Qco)G9!#9$"06:]\%\#\"!#7$"2()4$y")f#Hc"!#9$"2Gk1T-j,k"!#9$"1Vd)>i0Us"!#87;$"1R=aelU\9!#8$"1t1+ATjy8!#8$"1h],Tsk98!#8$"2d+&e:fYd7!#9$"2d]5d9!427!#9$"2:c"RJ*>N;"!#9$"2B<GEFbn7"!#9$"1R.Uphz'4"!#8$"271o<iUO2"!#9$"2"R8nHYHd5!#9$"2D<IJ>_x/"!#9$"27cW@J:]/"!#9$"2c]9n)R3\5!#9$"2d+So@e*f5!#9$"271@D+Qw2"!#9$"2@ndPMB@5"!#9$"2*Q)\0C9M8"!#9$"29c(*Gp5:<"!#9$"2$R3!3q7k@"!#9$"2DnfUE?"o7!#9$"2<1uKQLmK"!#9$"2a+Wy0_>R"!#9$"11&pzGwSY"!#8$"27c]O21Ia"!#9$"2F<()[TT(G;!#97;$"2d()QpY$zT8!#9$"2.AbPx$ps7!#9$"2*>r7O'*R57!#9$"2cdaS06\:"!#9$"2mePv-Gi5"!#9$"2P:wlb]V1"!#9$"2dFq6ky#H5!#9$"2M&*>8G75+"!#9$"1m=DqZ^&z*!#9$"1e(fGGi*['*!#9$"/K-^`Yq&*!#7$"1)>UZ(R-g&*!#9$"1dn,a"Qwh*!#9$"1no%)))yIV(*!#9$"1KDBzJ.P**!#9$"2cP<DS"))>5!#9$"2K0nE/lG0"!#9$"1(Gs$QUl#4"!#8$"1wIj*)*[#R6!#8$"2,U\kH\E>"!#9$"2-K@)e^&GD"!#9$"1w([ndm)>8!#8$"2uyJ-b$o$R"!#9$"2MNq#zgIu9!#9$"2dZkQ;M<c"!#97;$"2ry69L<EE"!#9$"2Fk&e"Q5_>"!#9$"2N0:t)*3Y8"!#9$"0-+'[J"33"!#7$"2DaSa'G#Q."!#9$"12iOy8QO**!#9$"1ND)yl*e-'*!#9$"1CW&H\`oL*!#9$"1s=e$)G<R"*!#9$"0([wHya4!*!#8$"1CM]J$yz%*)!#9$"1Pvz)QkW&*)!#9$"1.sk,g+H!*!#9$"1DC0qJgr"*!#9$"10K,%*eD#Q*!#9$"1Q&HN<k4m*!#9$"2F9g3!Gx+5!#9$"2r)G#*RZDU5!#9$"2t=TXBU04"!#9$"2G/:ZGNc9"!#9$"2TXW/*Q`27!#9$"21UH<0QiF"!#9$"2F%*p&oxu^8!#9$"22-m4/jSV"!#9$"2Rl<*oQ=B:!#97;$"2Ddg>:)*=@"!#9$"2#R>\XR=Y6!#9$"27')yXHvs3"!#9$"1R8A*>s^."!#8$"1BP>%fY()*)*!#9$"18'H<vEQ^*!#9$"1e5#[Yip>*!#9$"01oMt`"[*)!#8$"1:1nd0Sn()!#9$"1B(Gu$Hqa')!#9$"1&RUF(315')!#9$"1;;hjVZL')!#9$"1"RO+TV\s)!#9$"1Cn,7!oW)))!#9$"1:Ebp"[?6*!#9$"1cSk#)Qo2%*!#9$"01"H^^Pr(*!#8$"2;O\v>7.-"!#9$"2H<DbV#Hq5!#9$"2"Rl0H#yq7"!#9$"29YV"y&p1>"!#9$"2&Rfy#[m5E"!#9$"1tR)H%*o#Q8!#8$"2:cP(epFA9!#9$"11n/I048:!#87;$"2CB&eGfj*="!#9$"2,6uaY9c7"!#9$"2La=zb)Ro5!#9$"2B`=f?))z,"!#9$"1n2u%4MQu*!#9$"1o<&eoTeP*!#9$"1A$=D$[!f2*!#9$"1N/uMN-W))!#9$"1-"=Dz(>!o)!#9$"1A8&egFWe)!#9$"1,,uuHrc&)!#9$"1NW=**Q0(f)!#9$"1BV=z.X0()!#9$"1o(RZT->)))!#9$"0x]e+5k7*!#8$"1Bt^_J(*Q%*!#9$"1M%RZ&=f>)*!#9$"2-r^7hEo-"!#9$"2G.&e#f*\y5!#9$"2."RZH"yp8"!#9$"2NM=>AiA?"!#9$"2AL=*p=Nu7!#9$"2s(QZtqC`8!#9$"2o(\eKy%*Q9!#9$"2Aj^s9a9`"!#97;$"1ndGh1$e>"!#8$"2b:K:%>]L6!#9$"2**4Mtxyz2"!#9$"2.g"po6EH5!#9$"1cl/c6\t)*!#9$"1nEt!=EC_*!#9$"1LV(4w;%R#*!#9$"1e:x'*GYC!*!#9$"1NV7)ekv())!#9$"0nK]$=s)z)!#8$"1fl\PY$zy)!#9$".;b*H?X))!#6$"1,544p_q*)!#9$"1d:Ayj!R;*!#9$"1nw!HST`U*!#9$"1O$\J)>$[v*!#9$"1cY*="yB:5!#8$"2O$*H5)zzh5!#9$"2rw?dqj^6"!#9$"1cr'f)\Lv6!#8$"205p<#=JU7!#9$"21gEJ@%4;8!#9$"2jlR+;#o'R"!#9$"1n#3DmvS["!#8$"2QVK0su#y:!#97;$"2^<i+N#[I7!#9$"2`2mOPY)p6!#9$"24`DG&f,;6!#9$"1U0a(3"**o5!#8$"2*36"yxr(G5!#9$"13BPO-e`**!#9$"1(3*=]#)\(o*!#9$"1B9c>=Z*[*!#9$"16$*[W4]f$*!#9$"1aF(\i&e(H*!#9$"1`<,hes.$*!#9$"13jg_;#zP*!#9$"0Uc(**H<?&*!#8$"1)3iC!*z/t*!#9$"23LsgB%)3+"!#9$"2%3SXPg_N5!#9$"2>C"R%Rtp2"!#9$"28.%)oIE_7"!#9$"2dPK\x%G!="!#9$"2bFO&)z[@C"!#9$"28t&px$=3J"!#9$"2Bu5C^$H'Q"!#9$"2%48o-Udo9!#9$"1Ju][/md:!#8$"2'3"*))\Ab`;!#97;$"2&eW"\*4f$H"!#9$"2&pe(=wZYB"!#9$"2e$GR%35D="!#9$"2%e`Yiz<P6!#9$"2hV$4'R^')4"!#9$"2'pqF&QIp1"!#9$"2$ei,I\,U5!#9$"1.5JI]!R-"!#8$"1.8;'o+E,"!#8$"2'erc(*=535!#9$"2*p&GXm3/,"!#9$"2i`Xq)4_>5!#9$"2(e!=^')Qa."!#9$"2k8Y()Hi"e5!#9$"2'p(HzG"p(3"!#9$"2$e*oE$e-C6!#9$"2GqjH$f;n6!#9$"2J+9))e6r@"!#9$"2)e)>-!G'QF"!#9$"2%p7=n&>uL"!#9$"2lB)p*)=y29!#9$"2#f2xn(\\["!#9$"1P))R,K#*o:!#8$"2&pCe!>-(f;!#9$"2*e;KNnGd<!#97;$"2ehUefc^Q"!#9$"1Q:;1h!zK"!#8$"2f,O?<huF"!#9$"2"\gY$z@QB"!#9$"1Q;Xqz)p>"!#8$"2Hy#*Hqfp;"!#9$"2F[*3"*ptV6!#9$"2#Q<uM)>t7"!#9$"2#\&\RB3x6"!#9$"2c"Hr)=-\6"!#9$"2$Q=.*p,*=6!#9$"2eJ1\w1(H6!#9$"2$\jL'Q<t9"!#9$"1Q>KjNtr6!#8$"2G3jeHbH?"!#9$"2EyfRe#)4C"!#9$"2#Q?hFa"eG"!#9$"2)\)>o#QXP8!#9$"2l@$e"y(*eR"!#9$"2y8->HZ6Y"!#9$"1;mxdB?L:!#8$"2&\m?zH17;!#9$"2)QA>c"Hxp"!#9$"2FQL())3?!z"!#9$"1$3Io<y%*)=!#87;$"2ykYG:z^]"!#9$"293BlS@'\9!#9$"02bd@p3S"!#7$"2XhU0eA*e8!#9$"1:d)3]"yB8!#8$"2,P%ywfW&H"!#9$"28eQ#3g"RF"!#9$"2"[$[_f">f7!#9$"2,n8yts7D"!#9$"1[X$fVf,D"!#8$"2:)4h*o^eD"!#9$"2-(H%))\\$o7!#9$"2Z^IO'Gl(G"!#9$"2YhtRyhPJ"!#9$"2/Fs)finY8!#9$"29[E8H'R'Q"!#9$"2([iLy=#HV"!#9$"23d,4-`i["!#9$"2'[C->(*QY:!#9$"28)))ps>L8;!#9$"0(3$>yzqo"!#7$"1:%=n9Lww"!#8$"2[^hq1#*\&=!#9$"2/<gHac"\>!#9$"29Q9WdE,0#!#97;$"2NbEfmeOl"!#9$"2&)\gHm$z*f"!#9$"2')**\b@MFb"!#9$"2Q0&pB.[7:!#9$"2`m&R()>.z9!#9$"2<$=l1#*Q_9!#9$"1aNY")>bK9!#8$"2;$3$=J?&>9!#9$"2bm`x>%H89!#9$"1a?BRO(QT"!#8$"2))*fEO'e7U"!#9$"2')\b))=\aV"!#9$"1a0+(HXkX"!#8$"2a;,2'pC%["!#9$"2BLd*zT&)=:!#9$"2U0pZ&pEg:!#9$"1Kj8&G&[3;!#8$"1l"f5<4Nm"!#8$"2XbPDhQ`s"!#9$"2*)\r&4O(Rz"!#9$"1**4;iTTp=!#8$"2[01.Fg;&>!#9$"2dm1S$>rS?!#9$"2C$GE`"pl8#!#9$"1aX2G>BRA!#87;$"2WL#3N^fI=!#9$"0zta(GUy<!#7$"29!3Urh0L<!#9$"1oL#H-&\%p"!#8$"2)*[")*H%RFm"!#9$"2#o^f#R*yP;!#9$"1,Ww5\k>;!#8$"2.>*[%)fI3;!#9$"2W`pPhsPg"!#9$"2[V0')zWgg"!#9$"2.*o**QD7:;!#9$"2:!R%\$e+J;!#9$"2(okW'o%p`;!#9$"0f/N4*=$o"!#7$"1p#=h0*[><!#8$"27](GuXfi<!#9$"2-H7![c]7=!#9$"1NEHxAAp=!#8$"2b`G@YWF$>!#9$"22**>D?sI+#!#9$"28+n%)\0-3#!#9$"2'o&p*\V9k@!#9$"1"pFqv))[D#!#8$"2(o8k>(QCN#!#9$"1-1"yB%zcC!#87;$"2)*)RJg&))f.#!#9$"2h&H1W!4b)>!#9$"2#yuO$3N=%>!#9$"2lbF#ym'\!>!#9$"2(*=V'GQ!\(=!#9$"2(yVhMlk^=!#9$"2L7Thz%>N=!#9$"2GUBKh[b#=!#9$"2&y7'e)zqA=!#9$"0paS"HnE=!#7$"2ml.yRVu$=!#9$"2%y"3rV>]&=!#9$"2lDo>.,%z=!#9$"2(*)QQ#=)e5>!#9$"2%z]N))3e[>!#9$"2N#=))\"zL*>!#9$"1BT'p'H)\/#!#8$"2$z>gRBR.@!#9$"20R&znsgo@!#9$"1dVa^xiSA!#8$"1z)[3z`%>B!#8$"2y&*3dQ&30C!#9$"22fCh`Av\#!#9$"0y&4U_w'f#!#7$"1CDi.N"Gq#!#87;$"2y^@;%*Q)pA!#9$"1'*zso@0@A!#8$"2'H+R^42z@!#9$"2&=wg*G&*Q9#!#9$"2Gw!Q$=Db6#!#9$"2HY4FjgR4#!#9$"2'=PfP;?z?!#9$"2)HN.)>[72#!#9$"2k*)GSJ+,2#!#9$"1>)zb)zvv?!#8$"1(H'o77A)3#!#8$"2'H$[`***[2@!#9$"2)=fcLVcL@!#9$"2M1RtAWk;#!#9$"2PwnmnHh?#!#9$"1>?b"o?ED#!#8$"2.$=*>C<fI#!#9$"2k>()zN>gO#!#9$"2)>"Q&Hq#HV#!#9$"2wfWmDSm]#!#9$"0j1$R!fre#!#7$"0ACvP$[uE!#7$"1ktHrKhoF!#8$"1kgi?([&pG!#8$"1>.^D(*GxH!#87;$"2D#\+zi9KD!#9$"28"*o%\A0&[#!#9$"2cX)[vPwWC!#9$"1cN1d3G6C!#8$"16U>%\.YQ#!#8$"2AU!)ooJZO#!#9$"1*=A^Vl;N#!#8$"16&>*QZSXB!#8$"1*Qs#)f\fM#!#8$"1B3=8+I`B!#8$"29"[k$)fXnB!#9$"1cVm4vT)Q#!#8$"2dXR7f%=;C!#9$"296q$Gsv]C!#9$"2HKc5UN@\#!#9$"2%*3)Hp">.a#!#9$"17a4t%3`f#!#8$"1"H[CL.rl#!#8$"1CnNZPqDF!#8$"2:r?yr46!G!#9$"1c-%QC@L)G!#8$"2mN:aKQB(H!#9$"2B,YD'4;oI!#9$"1BABb"*yqJ!#8$"0*RZ.HA!G$!#77;$"20?kCd5H#G!#9$"/dG'G4vx#!#6$"2lvicb8*QF!#9$"2lO&f!QBrq#!#9$"2O`$3h(Q@o#!#9$"1cs7(pfRm#!#8$"2O`E()='e_E!#9$"1n8)eB=![E!#8$"2kv"fQeD]E!#9$"22qdo**)HfE!#9$"1,#z1rZ^n#!#8$"1ci0!)>!yp#!#8$"1n)))\!=EFF!#8$"2V.xa=FNw#!#9$"1d2_@")f1G!#8$"1N+78YZcG!#8$"1o[Fgm:8H!#8$"1c_)HEWm(H!#8$"29?^7UPp/$!#9$"1,F2Nh.CJ!#8$"1c(\WSSz?$!#8$"2&oBQH-l)H$!#9$"2c`q)4c;'R$!#9$"1dU"fa'[+N!#8$"1MN^PIh6O!#87;$"2EN**>#=8UJ!#9$"1j$y"zKU)4$!#8$"1JH">H?:1$!#8$"1`I?gGUJI!#8$"28t[S)483I!#9$"1k*\MmW;*H!#8$"1`nS)*Q'>)H!#8$"1)4>*)o)3zH!#8$"2u*p)\.>I)H!#9$"2PX5m$\v$*H!#9$"2PY*y$R'H6I!#9$"28.ClSVc.$!#9$"1`T"[(fzmI!#8$"2C$)f')4aZ5$!#9$"1m51yx^\J!#8$"2N&y,8q3,K!#9$"1)>IN!=YfK!#8$"1)4)f\@kCL!#8$"2`b@70GmR$!#9$"1l0S3&>aZ$!#8$"08N6_;5c$!#7$"1b_U*3>Ml$!#8$"2B$4F8si_P!#9$"1n@n#*3keQ!#8$"1a*Gw7g9(R!#87;$"2(y.hF+")*[$!#9$"2C!p9GUzZM!#9$"0)*QU)Re7M!#7$"2Ph')eHzTQ$!#9$"2D!)*3j,eiL!#9$"1Y&[ee'yZL!#8$"2j%G;k&)zRL!#9$"2EqK!)4;'QL!#9$"18"eu=RUM$!#8$"03RC$ymcL!#7$"1-c(H.-fP$!#8$"0on!*yT>S$!#7$"18`r+ryMM!#8$"1.&=z'zVuM!#8$"2kCx1R%*3_$!#9$"1[:**oj:uN!#8$"1-9'G!RAMO!#8$"18oG#*p4,P!#8$"2/ynsjvZx$!#9$"2CI/y$)f_&Q!#9$"1"Q'*Qf\D%R!#8$"19Sa0\kOS!#8$"10susdaPT!#8$"1[f]&>__C%!#8$"2vC?Q<k(fV!#97;$"20G(H*=Xf'Q!#9$"2WJ">L@iDQ!#9$"2W!4kKY5#z$!#9$"1[gk(o#RlP!#8$"1[n?)H'[XP!#8$"1/IKkaQKP!#8$"2V"[*f=!4EP!#9$"1"=AKY+ms$!#8$"1.^+'H;Rt$!#8$"1"eVVoP![P!#8$"1:wBGY'*oP!#8$"2L?(oFrp'z$!#9$"2vM#p#=N7$Q!#9$"1\ID$zyD(Q!#8$"10$p$fzs?R!#8$"1:6/"o#ovR!#8$"29[o#eHWPS!#9$"1090"z3g5%!#8$"1#))*Qz,Q"=%!#8$"1;RGBrbjU!#8$"2M]LFiRDN%!#9$"0lQxnF$[W!#7$"2&\$*H)G@4b%!#9$"2Mg:WX?.m%!#9$"1:u3w^_wZ!#87;$"2k0gqIP0F%!#9$"2<g6V*p!>B%!#9$"28q=rB#3+U!#9$"2jN"[NI1vT!#9$"2uc*R*Q\o:%!#9$"1ML())HTa9%!#8$"1dE!RwQ39%!#8$"2``([%yTI9%!#9$"1ozig.0_T!#8$"2u&RK#\ky;%!#9$"1,bdzT[!>%!#8$"1-EQA%4*>U!#8$"1d_u?-9cU!#8$"2%oMmul<*H%!#9$"1Ns8%[=!\V!#8$"1el;\fm0W!#8$"1O9vp*="pW!#8$"2(p=*eax$RX!#9$"2%eyex;W;Y!#9$"1,%R[O6.q%!#8$"2;]Ywg')4z%!#9$"1d"4gSn%))[!#8$"2%pt#*fPv#*\!#9$"1N6Spc%Q5&!#8$"1e/VMJu@_!#87;$"11()*3Q'e.Z!#8$"1jx]6)[mm%!#8$"2MPswz;lj%!#9$"1TDRR.>8Y!#8$"1j#omVpmf%!#8$"0a*\*3ape%!#7$"2YP')yHWSe%!#9$"1j(G=1Sze%!#8$"13nK"QT')f%!#8$"12-Qc#[hh%!#8$"2VE*)pog/k%!#9$"2O(Q:t'y:n%!#9$"21/u[@-&4Z!#9$"2Dw\@JJUv%!#9$"1T5)\'fw0[!#8$"2P(yOth5k[!#9$"2NE5t$>DH\!#9$"14#3oD.7+&!#8$"2%3<'=8g*z]!#9$"1l2ZiD_l^!#8$"1t`j[0*yD&!#8$"1TbN!4kqN&!#8$"1j7j(=VIY&!#8$"1TDYSy#ed&!#8$"1v$\)[!=ap&!#87;$"0B83T#4l^!#7$"1(zzZeZ)H^!#8$"2&>>I9$395&!#9$"2ufz$*fu(z]!#9$"1KG,Sk%\1&!#8$"2$>;?OQ#p0&!#9$"1mf%zy1d0&!#8$"1leC&H&Hh]!#8$"2.K,"e$*ot]!#9$"0L7l(*))G4&!#7$"1(*)y/:%*)=^!#8$"1@5+!)[q^^!#8$"1(py];@8>&!#8$"1K>r0IuP_!#8$"1B2!>Sq4H&!#8$"1m]k`L+^`!#8$"1m\%4'=%yT&!#8$"1@/!Q#f["\&!#8$"1M9@Ub$>d&!#8$"1)*z<;2>fc!#8$"1@,qX9D`d!#8$"1*zx2t<T&e!#8$"1K5Tr&*yhf!#8$"1A)*fnpEwg!#8$"1lTM>*\v>'!#87;$"1FO!oRb]l&!#8$"11x79L]@c!#8$"1Tt+(ycZf&!#8$"1HDW:e"[d&!#8$"1sKV*R!ohb!#8$"1v&z*Q0Nbb!#8$"0V"3Mi#eb&!#7$"1T)QZ[2Jc&!#8$"13=&4H%>xb!#8$"0L?Fl'3)f&!#7$"13W/qXyDc!#8$"1TS#H/)Ggc!#8$"1H#f82(f,d!#8$"1v*\`l6(\d!#8$"1vi*[zJY!e!#8$"1H")***[dj'e!#8$"1TblS())[$f!#8$"13&ooaD-,'!#8$"0.P'3zO#4'!#7$"126'f#eJ"='!#8$"0uS))HpqF'!#7$"0$fFF$G'zj!#7$"1umE6H**)['!#8$"1wH"30j^g'!#8$"1J["fuQ"Gn!#8-%+AXESLABELSG6%-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"m6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"b6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%+PROJECTIONG6,$"1wn(>q*****\!#;$!1/$\3pn52(!#;$"1wn(>q*****\!#;$"1wn(>q*****\!#;$"1/$\3pn52(!#;$"1wn(>q*****\!#;$!1/$\3pn52(!#;$""!!""$"1/$\3pn52(!#;$"#5!""-%&STYLEG6#%/SURFACECONTOURG-%*AXESSTYLEG6#%$BOXG-%%ROOTG6'-%)BOUNDS_XG6#$"$+"!""-%)BOUNDS_YG6#$"$+"!""-%-BOUNDS_WIDTHG6#$"%+R!""-%.BOUNDS_HEIGHTG6#$"%+R!""-%)CHILDRENG6"

sol:=solve({eq1,eq2},{m,b});

PCQvSSJiRzYiJCIrWyhwKVtPISM1L0kibUdGJSQhK0dWKUh3IiEiKg==

sol[1];

L0kiYkc2IiQiK1socClbTyEjNQ==

foundedLine:=x->subs(sol, m*x+b);

Zio2I0kieEc2IkYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUklc3Vic0clKnByb3RlY3RlZEc2JEkkc29sR0YlLCYqJkkibUdGJSIiIjkkRjFGMUkiYkdGJUYxRiVGJUYl

foundedLine(x);

LCZJInhHNiIkIStHVilIdyIhIiokIitbKHApW08hIzUiIiI=

Exercise: For the problems above, define a distance function by taking the absolute value of the vertical distances. Then try to minimize that distance. What happens?JSFHJSFH absValueDist:=(p,m,b)->abs(m*p[1]+b-p[2] );

Zio2JUkicEc2IkkibUdGJUkiYkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkYWJzRyUqcHJvdGVjdGVkRzYjLCgqJjklIiIiJjkkNiNGMkYyRjI5JkYyJkY0NiMiIiMhIiJGJUYlRiU=

E:=(data,m,b)->sum(absValueDist(data[i],m,b) , i=1..nops(data) );

Zio2JUklZGF0YUc2IkkibUdGJUkiYkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQtSS1hYnNWYWx1ZURpc3RHRiU2JSY5JDYjSSJpR0YlOSU5Ji9GNzsiIiItSSVub3BzR0YuNiNGNUYlRiVGJQ==

E(pts,m,b);

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

plot3d(E(pts,m,b),m=-3..2,b=0..2,style=patchcontour);

-%'PLOT3DG6&-%%GRIDG6%;$!#I!""$"#?!"";$""!!""$"#?!""7;7;$"2-+>J%3m#\"!#9$"2nm&y4v#=\"!#9$"2lmlp&[o"\"!#9$"2-+*H!>=D\"!#9$"1LBjB:N$\"!#8$"2lmlp&[=%\"!#9$".*H!>=]\"!#5$"1LBjB:&e\"!#8$"2lmlp&[o'\"!#9$".*H!>=v\"!#5$"1LBjB:N)\"!#8$"2lmlp&[=*\"!#9$".*H!>=+]"!#5$"1LBjB:&3]"!#8$"2lmlp&[o,:!#9$".*H!>=D]"!#5$"1LBjB:N.:!#8$"2lmlp&[=/:!#9$".*H!>=]]"!#5$"2LLKO_^e]"!#9$"2omlp&[o1:!#9$".*H!>=v]"!#5$"2LLKO_^$3:!#9$"2omlp&[=4:!#9$"2)***e4$)z,^"!#97;$"2lm!zGC7]7!#9$"2KLda4*G\7!#9$"2***R7idX[7!#9$"2lm!zGCiZ7!#9$"2)**R!oJZuC"!#9$"2MLP,l!G[7!#9$"2lmqM)R6\7!#9$"2)**R!oJZ*\7!#9$"2MLP,l!y]7!#9$"2lmqM)Rh^7!#9$"2)**R!oJZCD"!#9$"2MLP,l!G`7!#9$"2lmqM)R6a7!#9$"2)**R!oJZ\D"!#9$"2MLP,l!yb7!#9$"2imqM)Rhc7!#9$"2)**R!oJZuD"!#9$"2MLP,l!Ge7!#9$"2lmqM)R6f7!#9$"2(**R!oJZ*f7!#9$".9EOH7E"!#5$"2(**Rhi$HPE"!#9$"2(**Rhi$HiE"!#9$".9EOH(o7!#5$"2(**Rhi$H7F"!#97;$"2mm:p+)f45!#9$"2mm:p+)425!#9$"2im&zZt"f+"!#9$"2KLiW,%305!#9$"2)***G6o]U+"!#9$"2im&zZtT.5!#9$"2LLUmx4K+"!#9$"2kmv*4J//5!#9$"2&***3LWw[+"!#9$"2LLUmx4d+"!#9$"2kmv*4Ja15!#9$"2&***3LWwt+"!#9$"2LLUmx4#35!#9$"2kmv*4J/45!#9$"2&***3LWw)45!#9$"2LLUmx42,"!#9$"2)***oU*)yA,"!#9$"2&***oU*)yZ,"!#9$"2&***oU*)ys,"!#9$"2)***oU*)y(>5!#9$"2&***oU*)yA-"!#9$"2)***oU*)yZ-"!#9$"2&***oU*)ys-"!#9$"1LB'zw^/."!#8$"2)***GYV=Y."!#97;$"1)**R&o0rfx!#9$"1(**R&o0rMx!#9$"1#**R&o0r4x!#9$"1)**R&o0r%o(!#9$"1(**R&o0rfw!#9$"1#**R&o0rMw!#9$"1&**R&o0r4w!#9$"1im+oE7#f(!#9$"0m1[OA(*e(!#8$"1'**R")pb!)f(!#9$"1HLZJ!*Q1w!#9$"0m1[OAZh(!#8$"1(**R#fUGLw!#9$"1'**R#fUGew!#9$"1FL<Qd^*o(!#9$"1'**R[S#=Jx!#9$"1hm]r!\Gx(!#9$"1FL<Qd^9y!#9$"1'**R[S#=cy!#9$"1jm]r!\y*y!#9$"1GL<Qd^Rz!#9$"1)**R[S#=")z!#9$"1hm]r!\G-)!#9$"1GL<Qd^k!)!#9$"1)**R[S#=1")!#97;$"1&***[#3)3ec!#9$"29mc"\Zv*f&!#:$"2kKBeT@9a&!#:$"1&***[#3)3$[&!#9$"29mc"\ZvCa!#:$"21mcnjb@P&!#:$"1&***395wT`!#9$"1jmv!oFML&!#9$"2c***oEO>Q`!#:$"1hmDH@)4O&!#9$"1HLsn0f"R&!#9$"2b***QMsDLa!#:$"2Y***="palZ&!#:$"1GL_C!))[`&!#9$"1im&yN@Kf&!#9$"2Y***="pa:l&!#:$"1GL_C!)))4d!#9$"1im&yN@#od!#9$"1GLUdjyQe!#9$"2'GLUdjy8f!#:$"1GLUdjy))f!#9$"1GLUdjyjg!#9$"1GLUdjyQh!#9$"2lKBuN'y8i!#:$"1GLUdjy)G'!#97;$"1KL_z?T"[%!#9$"1mm&GTX(*Q%!#9$"2')***=Y(y!)H%!#:$"2')*\'4x+AA%!#:$"1L$)Ro2<jT!#9$"2')*\1Nu$[5%!#:$"1l;t,T]YS!#9$"1L$)Ro2<))R!#9$"1k;tc'G!QR!#9$"1mmDc1H5R!#9$"1**\Or(QB*Q!#9$"1l;)*>`#z*Q!#9$"1**\6+Da6R!#9$"1lm5aTf_R!#9$"1JLx?3E%*R!#9$"1JLPa(f)\S!#9$"0LBopqH7%!#8$"1k;8fK'>?%!#9$"1jm?_O#)=V!#9$"1km?_O#QW%!#9$"1km?_O#)oX!#9$"1jm?_O#Qp%!#9$"1jm?_O#)=[!#9$"2Cm1AlBQ%\!#:$"1jm?_O#)o]!#97;$"2'***R+w0N1%!#:$"2'***R+w0&QS!#:$"-/gd]8S!#5$"2'***R+w0&))R!#:$"2'***R+w0N'R!#:$"-/gd]QR!#5$"2'***R+w0N"R!#:$"2kmc&ev.(*Q!#:$"1nm?b=I$*Q!#9$"21+S&)=N;!R!#:$"21+!*p"f!G"R!#:$"-*p"f!y$R!#5$"21+!*p"f!G'R!#:$"21+!*p"f!y)R!#:$"1LL7s^w<S!#9$"1,+zQ=VfS!#9$"2vmca])4,T!#:$"2mmcu?e7:%!#:$"-zS:f4U!#5$"1****e.O-tU!#9$"1****e.O-[V!#9$"-f.O-BW!#5$"1****e.O-)\%!#9$"2CLB<We(zX!#:$"2&****Q3^UrY!#:7;$"1p;[:35NY!#9$"2D+:)[TVVY!#:$"2;+l]#3FhY!#:$"1,]1D3F'o%!#9$"2;+l]#3F6Z!#:$"2;+l]#3FOZ!#:$"1,]1D3FhZ!#9$"1pmXZ5b#z%!#9$"1NL79x@M[!#9$"29+!z!Q%)e([!#:$"1pmXZ5b<\!#9$"2kLBTr<#f\!#:$"29+!z!Q%)3+&!#:$"1pmXZ5bU]!#9$"1,]J\4H%4&!#9$"1N$[EGCE:&!#9$"1O$[%zAf:_!#9$"1O$[%zAf!H&!#9$"1M$[%zAfl`!#9$"1O$[%zAfSa!#9$"2XL[%zAf:b!#:$"1M$[%zAf!f&!#9$"2XL[%zAflc!#:$"2XL[%zAfSd!#:$"1M$[%zAf:e!#97;$"1OL#R8mCV'!#9$"1OL#R8muX'!#9$"1OL#R8mC['!#9$"1OL#R8mu]'!#9$"1OL#R8mC`'!#9$"1OL#R8mub'!#9$"1OL#R8mCe'!#9$"1OL#R8mug'!#9$"1OL#R8mCj'!#9$"1OL#R8mul'!#9$"1PL#R8mCo'!#9$"1OL#R8muq'!#9$"1OL#R8mCt'!#9$"1OL#R8muv'!#9$"1ML#R8mCy'!#9$"1OL#R8mu!o!#9$"1ML#R8mC$o!#9$"1ML#R8mu&o!#9$"1OLs0ix')o!#9$"-RsGWGp!#5$"1pmXz$ec)p!#9$"1OL_[8f]q!#9$"1ML_[8fDr!#9$"1QL_[8f+s!#9$"1QL_[8fvs!#97;$"-HD#R:o)!#5$"0nc>*e?t')!#8$"1NLieD([m)!#9$"-HD#Rll)!#5$"0nc>*e?[')!#8$"1NLieD()R')!#9$"-HD#R:j)!#5$"0nc>*e?B')!#8$"1NLieD([h)!#9$"1,+%\)=w;')!#9$"1OLF=_4D')!#9$"0n1;bGMj)!#8$"1-]r#3'p_')!#9$"1o;3h(=Gp)!#9$"1N$[xU&[M()!#9$"1-]T%4_hx)!#9$"1o;3h(=y"))!#9$"1N$[xU&[f))!#9$"1-]T%4_6!*)!#9$"1o;3h(=G%*)!#9$"1n;)y!4Z))*)!#9$"1.]@TU!o/*!#9$"1M$[XdP^5*!#9$"1n;)y!4Zj"*!#9$"1.]@TU!=A*!#97;$"1nc7CF:*4"!#8$"2NL#z!R>$)4"!#9$"20+fu0'[(4"!#9$"2OL2,gz")4"!#9$"2nmSM$H,*4"!#9$"21+unEY)*4"!#9$"2OL2,gz15"!#9$"2nmSM$H^,6!#9$"21+unEYB5"!#9$"2OL2,gzJ5"!#9$"2nmSM$H,/6!#9$"21+unEY[5"!#9$"2OL2,gzc5"!#9$"1n1WLH^16!#8$"21+unEYt5"!#9$"2OL2,gz"36!#9$"2pmSM$H,46!#9$"21+unEY)46!#9$"2OL2,gz16"!#9$"2ML(H%QBC6"!#9$"2TL(H%QB\6"!#9$"2NL(H%QBu6"!#9$".WJZ*G?6!#5$"2tm5)RhXC6!#9$"2OLid@Q$H6!#97;$"1n"3z&=6U8!#8$"2/]T7>XHM"!#9$"2O$[dC&yPM"!#9$"1n"3z&=hW8!#8$"2/]T7>XaM"!#9$"2O$[dC&yiM"!#9$"1n"3z&=6Z8!#8$"2/]T7>XzM"!#9$"2O$[dC&y([8!#9$"1n"3z&=h\8!#8$"2/]T7>X/N"!#9$"2O$[dC&y7N"!#9$"1n"3z&=6_8!#8$"2/]T7>XHN"!#9$"2R$[dC&yPN"!#9$"1n"3z&=ha8!#8$"2/]T7>XaN"!#9$"2R$[dC&yiN"!#9$"1n"3z&=6d8!#8$"2/]T7>XzN"!#9$"2R$[dC&y(e8!#9$"1n"3z&=hf8!#8$"2ombb-41O"!#9$"1ncbD!4JO"!#8$"1ncBbE%fO"!#87;$"21+4d6W&)e"!#9$"2PLU!\uP*e"!#9$"1ncP#y5-f"!#8$"21+4d6W5f"!#9$"2PLU!\u(=f"!#9$"1ncP#y5Ff"!#8$"21+4d6WNf"!#9$"2PLU!\uP%f"!#9$"1ncP#y5_f"!#8$"21+4d6Wgf"!#9$"2PLU!\u(of"!#9$"1ncP#y5xf"!#8$"21+4d6W&)f"!#9$"2PLU!\uP*f"!#9$"1ncP#y5-g"!#8$"21+4d6W5g"!#9$"2PLU!\u(=g"!#9$"1ncP#y5Fg"!#8$"2.+4d6WNg"!#9$"2PLU!\uP/;!#9$"1ncP#y5_g"!#8$"2/+></Btg"!#9$"2/+></B)4;!#9$"2/+></BBh"!#9$"2/+></B[h"!#97;$"2N$)4NPw\$=!#9$"1nJ%oq4e$=!#8$"22]w,/Vm$=!#9$"2N$)4NPwu$=!#9$"1nJ%oq4$Q=!#8$"22]w,/V"R=!#9$"2N$)4NPw*R=!#9$"1nJ%oq43%=!#8$"22]w,/V;%=!#9$"2N$)4NPwC%=!#9$"1nJ%oq4L%=!#8$"22]w,/VT%=!#9$"2N$)4NPw\%=!#9$"1nJ%oq4e%=!#8$"22]w,/Vm%=!#9$"2N$)4NPwu%=!#9$"1nJ%oq4$[=!#8$"22]w,/V"\=!#9$"2N$)4NPw*\=!#9$"2PL#)y0P:&=!#9$"2PL#)y0PS&=!#9$"2ML#)y0Pl&=!#9$"1MB)y0P!f=!#8$"2UL#)y0P:'=!#9$"2ML#)y0PS'=!#97;$"1n1JJ'393#!#8$"2-+WY'>C#3#!#9$"2ULxzHvI3#!#9$"1n1JJ'3R3#!#8$"2-+WY'>u%3#!#9$"2ULxzHvb3#!#9$"1n1JJ'3k3#!#8$"2-+WY'>C(3#!#9$"2ULxzHv!)3#!#9$"1n1JJ'3*)3#!#8$"2-+WY'>u*3#!#9$"2ULxzHv04#!#9$"1n1JJ'394#!#8$"2-+WY'>C#4#!#9$"1Mt(zHvI4#!#8$"1n1JJ'3R4#!#8$"2-+WY'>u%4#!#9$"2vmXS2^d4#!#9$"1nc/u5D)4#!#8$"1nc/u5v+@!#8$"2vmXS2^K5#!#9$"1nc/u5v0@!#8$"1nc/u5D3@!#8$"2vmXS2^26#!#9$"1nc/u5D8@!#87;$"2/]6"*)3%yK#!#9$"2N$[WAUnGB!#9$"2v;ydb2&HB!#9$"2/]6"*)3MIB!#9$"2N$[WAU<JB!#9$"2v;ydb2?L#!#9$"2/]6"*)3%GL#!#9$"2N$[WAUnLB!#9$"2v;ydb2XL#!#9$"2/]6"*)3MNB!#9$"2N$[WAU<OB!#9$"2v;ydb2qL#!#9$"2/]6"*)3%yL#!#9$"2N$[WAUnQB!#9$"2v;ydb2&RB!#9$"2/]6"*)3MSB!#9$"2-+4-4lCM#!#9$"23+4-4l\M#!#9$"2-+4-4luM#!#9$"2-+4-4l*\B!#9$"23+4-4lCN#!#9$"2-+4-4l\N#!#9$".4-4luN#!#5$"23+4-4l*fB!#9$"2-+4-4lCO#!#97;$"2LL7p9tUd#!#9$"2wmX-[1^d#!#9$"1,!zN")Rfd#!#8$"2LL7p9tnd#!#9$"2wmX-[1wd#!#9$"1,!zN")R%yD!#8$"2LL7p9t#zD!#9$"2wmX-[1,e#!#9$"1,!zN")R4e#!#8$"2LL7p9t<e#!#9$"1ncC![1Ee#!#8$"1,!zN")RMe#!#8$"2LL7p9tUe#!#9$"2wmX-[1^e#!#9$"1MBP1"zme#!#8$"1MBP1"z"*e#!#8$"2VLsj5z;f#!#9$"1MBP1"zTf#!#8$"1MBP1"zmf#!#8$"1MBP1"z"*f#!#8$"1MBP1"z;g#!#8$"1MBP1"zTg#!#8$"1MBP1"zmg#!#8$"1MBP1"z"4E!#8$"1MBP1"z;h#!#87;$"1nJr/aq?G!#8$"/l/Q(Q:#G!#6$"2V$)z82sB#G!#9$"1nJr/a?BG!#8$"/l/Q(QS#G!#6$"2V$)z82s[#G!#9$"1nJr/aqDG!#8$"/l/Q(Ql#G!#6$"2V$)z82st#G!#9$"1nJr/a?GG!#8$"/l/Q(Q!HG!#6$"2V$)z82s)HG!#9$"2tmND7$*3$G!#9$"1nc`AJRLG!#8$"2tmND7$*e$G!#9$"2tmND7$RQG!#9$"2tmND7$*3%G!#9$"2tmND7$RVG!#9$"2tmND7$*e%G!#9$"2tmND7$R[G!#9$"2tmND7$*3&G!#9$"2tmND7$R`G!#9$"2tmND7$*e&G!#9$"2tmND7$ReG!#9$"1nc`AJ*3'G!#87;$"20+9DmPr1$!#9$"2OLZe*4(z1$!#9$"2tm!=HV!)oI!#9$"20+9DmP'pI!#9$"2OLZe*4ZqI!#9$"2tm!=HVIrI!#9$"20+9DmP@2$!#9$"2OLZe*4(H2$!#9$"2tm!=HV!Q2$!#9$"20+9DmPY2$!#9$"2OLZe*4ZvI!#9$"1,!*pQrgxI!#8$"1,!*pQr5!3$!#8$"2.+*pQrg#3$!#9$"1,!*pQr5&3$!#8$"2.+*pQrg(3$!#9$"2.+*pQr5!4$!#9$"1,!*pQrg#4$!#8$"2.+*pQr5&4$!#9$"2.+*pQrg(4$!#9$"1,!*pQr5+J!#8$"2.+*pQrg-J!#9$"1,!*pQr50J!#8$"1,!*pQrg2J!#8$"2.+*pQr55J!#97;$"1M[J?*pNJ$!#8$"2$o"[OD.WJ$!#9$"2.]")peO_J$!#9$"1M[J?*pgJ$!#8$"2$o"[OD.pJ$!#9$"2.]")peOxJ$!#9$"1M[J?*p&=L!#8$"2$o"[OD.%>L!#9$"2.]")peO-K$!#9$"2WLi[:@=K$!#9$"1NB'[:@VK$!#8$"2LLi[:@oK$!#9$"2WLi[:@$HL!#9$"1NB'[:@=L$!#8$"2LLi[:@VL$!#9$"1MB'[:@oL$!#8$"1NB'[:@$RL!#8$"2LLi[:@=M$!#9$"1MB'[:@VM$!#8$"1NB'[:@oM$!#8$"2LLi[:@$\L!#9$"1MB'[:@=N$!#8$"1NB'[:@VN$!#8$"2LLi[:@oN$!#9$"1MB'[:@$fL!#87;$"1nc6y@+gN!#8$"22+\9^N3c$!#9$"1MByW)o;c$!#8$"1nc6y@]iN!#8$"22+\9^NLc$!#9$"1MByW)oTc$!#8$"1nc6y@+lN!#8$"2umD5<Ngc$!#9$"2umD5<N&oN!#9$"1oc-r^.rN!#8$"2umD5<NNd$!#9$"2umD5<Ngd$!#9$"1oc-r^`yN!#8$"2umD5<N5e$!#9$"2umD5<NNe$!#9$"1oc-r^.'e$!#8$"2umD5<N&)e$!#9$"2umD5<N5f$!#9$"2umD5<NNf$!#9$"2umD5<Ngf$!#9$"2umD5<N&)f$!#9$"2umD5<N5g$!#9$"2umD5<NNg$!#9$"2umD5<Ngg$!#9$"1nc-r^`3O!#87;$"/l"fVMk!Q!#6$"1M)\#pxE2Q!#8$"1mJe-653Q!#8$"/l"fVM*3Q!#6$"1M)\#pxw4Q!#8$"1mJe-6g5Q!#8$"2/+*=(=\F"Q!#9$"2/+*=(=\_"Q!#9$".*=(=\x"Q!#5$"2/+*=(=\-#Q!#9$"2/+*=(=\F#Q!#9$".*=(=\_#Q!#5$"2/+*=(=\x#Q!#9$"2/+*=(=\-$Q!#9$".*=(=\F$Q!#5$"2/+*=(=\_$Q!#9$"2:+*=(=\x$Q!#9$".*=(=\-%Q!#5$"2/+*=(=\F%Q!#9$"2:+*=(=\_%Q!#9$".*=(=\x%Q!#5$"2/+*=(=\-&Q!#9$"1,!*=(=\F&Q!#8$".*=(=\_&Q!#5$"2/+*=(=\x&Q!#97;$"2NL<PpmG0%!#9$"1o10F+q`S!#8$".%QgL`aS!#5$"2NL<Ppm`0%!#9$"1MBN.K'p0%!#8$"2ML_L?j%fS!#9$"2XL_L?j>1%!#9$"1MBN.KYkS!#8$"2ML_L?jp1%!#9$"2XL_L?j%pS!#9$"1MBN.K'>2%!#8$"2ML_L?jW2%!#9$"2XL_L?jp2%!#9$"1MBN.KYzS!#8$"1LBN.K'>3%!#8$"2XL_L?jW3%!#9$"2XL_L?jp3%!#9$"1LBN.KY*3%!#8$"2ML_L?j>4%!#9$"2XL_L?jW4%!#9$"1LBN.K'p4%!#8$"2ML_L?j%*4%!#9$"2XL_L?j>5%!#9$"1LBN.KY/T!#8$"2ML_L?jp5%!#97;$"1n"=:&*)H*H%!#8$"1,:&[GK,I%!#8$"1lc^>s<,V!#8$"2vm:&>sn.V!#9$"2vm:&>s<1V!#9$"1lc^>sn3V!#8$"2vm:&>s<6V!#9$"2vm:&>sn8V!#9$"1lc^>s<;V!#8$"2vm:&>sn=V!#9$"2vm:&>s<@V!#9$"1lc^>snBV!#8$"2vm:&>s<EV!#9$"2vm:&>snGV!#9$"1lc^>s<JV!#8$"2vm:&>snLV!#9$"1oc^>s<OV!#8$"1lc^>snQV!#8$"2vm:&>s<TV!#9$"1oc^>snVV!#8$"1lc^>s<YV!#8$"2vm:&>sn[V!#9$"1oc^>s<^V!#8$"1lc^>sn`V!#8$"2km:&>s<cV!#97;$".>$47tXX!#5$"1,!zcB"*ya%!#8$"1,!zcB"R]X!#8$".zcB"*Gb%!#5$"1,!zcB"RbX!#8$"1,!zcB"*yb%!#8$".zcB"RgX!#5$"1,!zcB"*Gc%!#8$"1,!zcB"RlX!#8$".zcB"*yc%!#5$"1,!zcB"RqX!#8$"1,!zcB"*Gd%!#8$".zcB"RvX!#5$"1,!zcB"*yd%!#8$"1,!zcB"R!e%!#8$".zcB"*Ge%!#5$"1,!zcB"R&e%!#8$"1,!zcB"*ye%!#8$".zcB"R!f%!#5$"1,!zcB"*Gf%!#8$"20+zcB"R&f%!#9$".zcB"*yf%!#5$"1,!zcB"R+Y!#8$"20+zcB"*Gg%!#9$".zcB"R0Y!#5-%+PROJECTIONG6,$"1aa@!eD(\F!#;$!1i#ou@=Eg*!#;$"1Nb%G*>5%y%!#<$"1ZGa4O7Oz!#;$"2P!QF'>#zZD!#<$"0bjKU,^_&!#:$!1pO#epEuU&!#;$!2)=O>wxdR6!#<$"1'GooeC8K)!#;$"#5!""-%&STYLEG6#%/SURFACECONTOURG-%%ROOTG6'-%)BOUNDS_XG6#$"$+"!""-%)BOUNDS_YG6#$"$+"!""-%-BOUNDS_WIDTHG6#$"%+R!""-%.BOUNDS_HEIGHTG6#$"%+R!""-%)CHILDRENG6"

First try "blindly" to repeat what we did before. eqm:=diff(E(pts,m,b),m); eqb:=diff(E(pts,m,b),b);

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

plot3d(E(pts,m,b),m=-2..-1.6,b=0..2,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-2..-1.6,b=0..2,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-1.95..-1.8,b=0.5..1.5,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-1.95..-1.8,b=0.7..1.2,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-1.905..-1.85,b=0.8..1.05,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-1.905..-1.86,b=0.8..0.95,axes=boxed, style=patchcontour); plot3d(E(pts,m,b),m=-1.904..-1.886,b=0.8..0.9,axes=boxed, style=patchcontour); From the above picture we deduce that the minimum of E is when m is between -1.904 and -1.886 and b is between 0.8 and 0.9. EXERCISE: Consider the points newpts := [seq([i, 1.5*i+1], i = -1 .. 5), [8, 1.5*8+.5], seq([i, 1.5*i+1], i = 9 .. 11)]; a. Find a polynomial passing through those points. b. Fit the points with a line using the least squares method. Use the graph of the previous exercise to visualize the line you found, and see how "close" the line and the points are. c. Fit the points with a quadratic function using the least squares method. d. Find a piecewise linear function passing through all the points. e. Plot the points and all the functions together. f. Compare the results. In particular, compute the value of the function you found in each case when x=12.3 newpts := [seq([i, 1.5*i+1], i = -1 .. 5), [8, 1.5*8+.5], seq([i, 1.5*i+1], i = 9 .. 11)];

Ny03JCEiIiQhIiZGJDckIiIhJCIiIkYoNyRGKiQiI0RGJDckIiIjJCIjU0YkNyQiIiQkIiNiRiQ3JCIiJSQiI3FGJDckIiImJCIjJilGJDckIiIpJCIkRCJGJDckIiIqJCIkWCJGJDckIiM1JCIkZyJGJDckIiM2JCIkdiJGJA==

plot(newpts,style=point,symbol=solidbox,symbolsize=16);

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

with(CurveFitting): pol:=PolynomialInterpolation(newpts,x);

LDgqJEkieEc2IiIjNSQiK2FsKUdmJSEjOyokRiQiIiokISslM3EzLSMhIzkqJEYkIiIpJCIrI1woeUJPISM4KiRGJCIiKCQhK3BZMzFNISM3KiRGJCIiJyQiKyMpcCwkeiIhIzYqJEYkIiImJCErIjMmKmU7JkY9KiRGJCIiJSQiK2M8JTQjb0Y9KiRGJCIiJCQiKD92QCYhIzUqJEYkIiIjJCErTURDXScpRj1GJCQiKyNcalhiIiEiKiRGJiEiIiIiIg==

line:=LeastSquares(newpts,x);

LCYkIitDLF8lKSoqISM1IiIiSSJ4RzYiJCIrdT9yIVwiISIq

display(plot({line,pol},x=-1..20,thickness=3,color=[blue,green]),plot(newpts,style=point,symbol=solidbox,symbolsize=16));

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

quad:=LeastSquares(newpts,x,curve=a*x^2+b*x+c);

LCgkIitQUXBANSEiKiIiIkkieEc2IiQiK2tOJ29ZIkYlKiRGJyIiIyQiKywlXEdMIyEjNw==

spl:=Spline(newpts,x,degree=1);

LUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzY1MkkieEc2IiIiISwmJCIiIkYpRixGJyQiIzohIiIyRidGLEYqMkYnIiIjLCYkIiM1Ri9GLEYnRi0yRiciIiRGMzJGJyIiJUYzMkYnIiImRjMyRiciIiksJiQiK0xMTEw9ISIqRixGJyQiK0xMTEw4RkEyRiciIiosJiQhI05GL0YsRickIiM/Ri8yRidGNUYzRjM=

display(plot({line,pol,quad,spl},x=-1..11,thickness=3,color=[blue,green,cyan,brown]),plot(newpts,style=point,symbol=solidbox,symbolsize=16));

-%%PLOTG6,-%'CURVESG6%7S7$$!#5!""$!1*****fh+E#\!#;7$$!):M%Q(!")$!2/F*e3pSB5!#<7$$!+D5Z3^!#5$"1XLN(og#pB!#;7$$!*l;!\D!"*$"1pz,F-n%='!#;7$$"2%)3+++X.u#!#>$"2dUyx2PD+"!#;7$$"2%*****\Fy:f#!#<$"2#fe#\r"y%Q"!#;7$$"1*****\d'*)o\!#;$"2Y(4GC9<R<!#;7$$"1*****\(>ZIu!#;$"2C6l7W@h5#!#;7$$"+vnBw**!#5$"1Kvvt;i&[#!#:7$$",vs$Q^7!#5$"2dP">W[!R'G!#;7$$"2-+++82C^"!#;$"1)o%*=e:ID$!#:7$$"+&o;Bu"!"*$"2X:h9`Wdf$!#;7$$"*RS6+#!")$"2$p?a`hd")R!#;7$$"*&o-hA!")$"1(=Lt.#**oV!#:7$$"*hv9^#!")$"1:NyF!RBu%!#:7$$",v22*QF!#5$"1/LRiQP"3&!#:7$$"*4X$4I!")$"1;c*G2>X[&!#:7$$"*cT%QK!")$"1&RNo%f.Ee!#:7$$",v@N\]$!#5$"1m]rf7IBi!#:7$$"2(******fs#3u$!#;$"1P.jv$[\d'!#:7$$"2.++v@Q'**R!#;$"1)3f[*4wgp!#:7$$",DX(3YU!#5$"1_;5Xe9Gt!#:7$$"+v8B.X!"*$"1A"G^Rt9r(!#:7$$",vwp$RZ!#5$"1BG'zu([j!)!#:7$$"+Dp2%*\!"*$"1$H#)Hy#=V%)!#:7$$",v2Y'e_!#5$"0*>-8#zv$))!#97$$",DIa*)[&!#5$"1)*4xkC!4=*!#:7$$"+&\$pPd!"*$"1fxI#)4q^&*!#:7$$"*UlY*f!")$"0G%eL@xM**!#97$$"+:B1Yi!"*$"1*oK?D`4."!#97$$",vt,$*['!#5$"2H/KkC8s1"!#:7$$"+XwPfn!"*$"2%=F0)ytu5"!#:7$$"1******fG0-q!#:$"1B)e`n\O9"!#97$$"*Xg6E(!")$"2tiYm:vA="!#:7$$"2&****\P/&f\(!#;$"1$ooNevs@"!#97$$"1,++5zj_x!#:$"2Er=]HSbD"!#:7$$"1****\<3;%*z!#:$"2f\akSW:H"!#:7$$",v%=iY#)!#5$"2O/=q2z"H8!#:7$$"*l[M\)!")$"/a[YQ(fO"!#77$$",vV`=v)!#5$"2a'f:gX\/9!#:7$$"*'zs+!*!")$"1Rhr&e%fT9!#97$$"+0"Q_D*!"*$"1QoK?Z`z9!#97$$",vxSw]*!#5$"2)*Rn9pgr^"!#:7$$"*is&R(*!")$"2:Qj70N<b"!#:7$$",&o#R0+"!"*$"2y2/$p6O"f"!#:7$$"+KXJC5!")$"2#fgmTK!oi"!#:7$$"-v@Rm\5!#5$"2k"\.$)=fk;!#:7$$"-DAl#R2"!#5$"2[!paM/w+<!#:7$$"$5"!""$"-k#[G'R<!#5-%&COLORG6&%$RGBG$""!!""$""!!""$"#5!""-%*THICKNESSG6#""$-%'CURVESG6%7S7$$!#5!""$!29+!*fxo$GW!#<7$$!):M%Q(!")$!2m*[pFWi@g!#=7$$!+D5Z3^!#5$"1**zcqifHF!#;7$$!*l;!\D!"*$"1O/p([%Rzk!#;7$$"2%)3+++X.u#!#>$"20!=vmNrD5!#;7$$"2%*****\Fy:f#!#<$"2.?N@p**>S"!#;7$$"1*****\d'*)o\!#;$"1CL()\"R6v"!#:7$$"1*****\(>ZIu!#;$"2`vW"32$H6#!#;7$$"+vnBw**!#5$"2FyxaV$R([#!#;7$$",vs$Q^7!#5$"1-x<$=c4'G!#:7$$"2-+++82C^"!#;$"2N(>4_[_XK!#;7$$"+&o;Bu"!"*$"16M7ak^%e$!#:7$$"*RS6+#!")$"2(4,h.eVmR!#;7$$"*&o-hA!")$"13'\@$yB]V!#:7$$"*hv9^#!")$"0c,:P+/s%!#97$$",v22*QF!#5$"1Q'y^'pzc]!#:7$$"*4X$4I!")$"1Ut[`">rX&!#:7$$"*cT%QK!")$"19%>B`6lz&!#:7$$",v@N\]$!#5$"1$[Zbl8;>'!#:7$$"2(******fs#3u$!#;$"1&*)R_WA;a'!#:7$$"2.++v@Q'**R!#;$"1*G"GYi$f#p!#:7$$",DX(3YU!#5$"1Q>)eN%=#H(!#:7$$"+v8B.X!"*$"0ez2$ziuw!#97$$",vwp$RZ!#5$"10eabA5E!)!#:7$$"+Dp2%*\!"*$"1KRaak]0%)!#:7$$",v2Y'e_!#5$"1;#G]G@**z)!#:7$$",DIa*)[&!#5$"0um$Rk_V"*!#97$$"+&\$pPd!"*$"0n$y'R2\^*!#97$$"*UlY*f!")$"1&HJvU$)))*)*!#:7$$"+:B1Yi!"*$"2i!>f?F[F5!#:7$$",vt,$*['!#5$"2Vc2>G&)Q1"!#:7$$"+XwPfn!"*$"2FNI5YOV5"!#:7$$"1******fG0-q!#:$"2m7?Fn729"!#:7$$"*Xg6E(!")$"1Q%ePP#ez6!#97$$"2&****\P/&f\(!#;$"2p$*3B:J[@"!#:7$$"1,++5zj_x!#:$"2,)p+3oR`7!#:7$$"1****\<3;%*z!#:$"0y@b:7(*G"!#87$$",v%=iY#)!#5$"1'[E3D,xK"!#97$$"*l[M\)!")$"2u)=u%Gr[O"!#:7$$",vV`=v)!#5$"2o'\&=K:QS"!#:7$$"*'zs+!*!")$"2(='p,^_8W"!#:7$$"+0"Q_D*!"*$"1;()[%fp(z9!#97$$",vxSw]*!#5$"2->jQT)*y^"!#:7$$"*is&R(*!")$"2TPlW/hHb"!#:7$$",&o#R0+"!"*$"2'y>XUw<$f"!#:7$$"+KXJC5!")$"2F(zKxd<H;!#:7$$"-v@Rm\5!#5$"2&RD#yM'en;!#:7$$"-DAl#R2"!#5$"20NVdCyVq"!#:7$$"$5"!""$"/@&=yYRu"!#7-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%*THICKNESSG6#""$-%'CURVESG6%7V7$$!#5!""$!1YIU(*******\!#;7$$!):M%Q(!")$!1,Y*>7'\.;!#;7$$!+D5Z3^!#5$"2=v*zH(e+!>!#<7$$!*l;!\D!"*$"1=BY)p(e%)f!#;7$$"2%)3+++X.u#!#>$"/zr!RfU+"!#87$$"2%*****\Fy:f#!#<$"2f?G))4HtR"!#;7$$"1*****\d'*)o\!#;$"2&)y^b3#*Rv"!#;7$$"1*****\(>ZIu!#;$"2xFj*oSG>@!#;7$$"+vnBw**!#5$"2[,mxJtk\#!#;7$$",vs$Q^7!#5$"2lfm->wT(G!#;7$$"2-+++82C^"!#;$"2W;ibl<_E$!#;7$$"+&o;Bu"!"*$"2`H#e?2K6O!#;7$$"*RS6+#!")$"1he?&3?<+%!#:7$$"*&o-hA!")$"2:P)G>%GLR%!#;7$$"*hv9^#!")$"1,^P!e]&pZ!#:7$$",v22*QF!#5$"0&*poP]+6&!#97$$"*4X$4I!")$"1cL'*H$[R^&!#:7$$"*cT%QK!")$"12L`M?(f&e!#:7$$",v@N\]$!#5$"2&\([:spYD'!#;7$$"2(******fs#3u$!#;$"1wUy)o&**3m!#:7$$"2.++v@Q'**R!#;$"1sx6eJX**p!#:7$$",DX(3YU!#5$"1kZ&e0<BP(!#:7$$"+v8B.X!"*$"1WX%fhq3w(!#:7$$",vwp$RZ!#5$"1ohQLP2:")!#:7$$"+Dp2%*\!"*$"0'\TIzM"\)!#97$$",v2Y'e_!#5$"0'=r[+Es))!#97$$",DIa*)[&!#5$"1EjJC#3H>*!#:7$$"+&\$pPd!"*$"1Z-H?6!e_*!#:7$$"*UlY*f!")$"1i!\`)pWa)*!#:7$$"+:B1Yi!"*$"2C>:OCNi,"!#:7$$",vt,$*['!#5$"2P#*[)pS5X5!#:7$$"+XwPfn!"*$"2TS'p#\*zw5!#:7$$"1******fG0-q!#:$"2Lr))*oc!e5"!#:7$$"*Xg6E(!")$"2Q_^v](RQ6!#:7$$"2&****\P/&f\(!#;$"2d\uGjG.<"!#:7$$"1,++5zj_x!#:$"2dB/_Z"z37!#:7$$"1****\<3;%*z!#:$"2;`#p>"y*[7!#:7$$",v%=iY#)!#5$"2RcIo#QG&H"!#:7$$"*l[M\)!")$"2s(=]:HHW8!#:7$$",vV`=v)!#5$"2E'=)f$)G")R"!#:7$$"*'zs+!*!")$"2Gz(fi(\,X"!#:7$$"+0"Q_D*!"*$"2ac4S5*R+:!#:7$$",vxSw]*!#5$"2#p]s)y2Qa"!#:7$$"*is&R(*!")$"1#HA_1*Rv:!#97$$",&o#R0+"!"*$"2GH8%)=&R+;!#:7$$"+KXJC5!")$"2.E=Aa7Yh"!#:7$$".voA*)p."!#6$"2il5gb,8i"!#:7$$"-v@Rm\5!#5$"1r,0.HqH;!#97$$"+A_zh5!")$"2X:yXg')=k"!#:7$$"-DAl#R2"!#5$"1)=!)>OK9m"!#97$$"2,+D6Ejp3"!#:$"1sTDr^b&p"!#97$$"$5"!""$"2O5>'41+]<!#:-%&COLORG6&%$RGBG$""!!""$"#5!""$"#5!""-%*THICKNESSG6#""$-%'CURVESG6%7S7$$!#5!""$!"&!""7$$!):M%Q(!")$!2-+++D7l2"!#<7$$!+D5Z3^!#5$"2.++DY$HPB!#<7$$!*l;!\D!"*$"+D]Zwh!#57$$"2%)3+++X.u#!#>$",v^5T+"!#57$$"2%*****\Fy:f#!#<$"2)***\7uO()Q"!#;7$$"1*****\d'*)o\!#;$"-D'[M`u"!#67$$"1*****\(>ZIu!#;$"2)***\izqX6#!#;7$$"+vnBw**!#5$"-D;bV'\#!#67$$",vs$Q^7!#5$"2(***\7fvq(G!#;7$$"2-+++82C^"!#;$"20++]p5'oK!#;7$$"+&o;Bu"!"*$",v-vMh$!#57$$"*RS6+#!")$"20++]e5<+%!#;7$$"*&o-hA!")$"+v-a"R%!"*7$$"*hv9^#!")$"20++]T8sw%!#;7$$",v22*QF!#5$"-D;1O3^!#67$$"*4X$4I!")$"+Nw,9b!"*7$$"*cT%QK!")$"*Miw&e!")7$$",v@N\]$!#5$"-DEGSdi!#67$$"2(******fs#3u$!#;$"2&*******)3C6m!#;7$$"2.++v@Q'**R!#;$"1,+DEtX**p!#:7$$",DX(3YU!#5$"1,+vy68pt!#:7$$"+v8B.X!"*$"21++D1Z[v(!#;7$$",vwp$RZ!#5$"-D^Y04")!#67$$"+Dp2%*\!"*$"1****\(Q:6\)!#:7$$",v2Y'e_!#5$"0X!eM9'[%))!#97$$",DIa*)[&!#5$"1:q$y1R>:*!#:7$$"+&\$pPd!"*$"1o2UC8f$[*!#:7$$"*UlY*f!")$"1W%owb?i#)*!#:7$$"+:B1Yi!"*$"2XYe<kTh,"!#:7$$",vt,$*['!#5$"2lN]Zct&[5!#:7$$"+XwPfn!"*$"1a8u&o$e%3"!#97$$"1******fG0-q!#:$"1)fm5QSp6"!#97$$"*Xg6E(!")$"2ziC(f!)[^6!#:7$$"2&****\P/&f\(!#;$"2#oMQ"R$z#="!#:7$$"1,++5zj_x!#:$"2aC3xQ=q@"!#:7$$"1****\<3;%*z!#:$"2y_L?W@#\7!#:7$$",v%=iY#)!#5$",&pVK*H"!"*7$$"*l[M\)!")$"2*******H(*o[8!#:7$$",vV`=v)!#5$"2*****\(oq.S"!#:7$$"*'zs+!*!")$"2-++S>4,X"!#:7$$"+0"Q_D*!"*$"-v:dG)["!#57$$",vxSw]*!#5$"2,+Dm6Yh_"!#:7$$"*is&R(*!")$"+$*e$4c"!")7$$",&o#R0+"!"*$"-v-*33g"!#57$$"+KXJC5!")$"+)zrkj"!")7$$"-v@Rm\5!#5$".DE)e\u;!#67$$"-DAl#R2"!#5$".vLy*)3r"!#67$$"$5"!""$"$v"!""-%&COLORG6&%$RGBG$"1_MmX%)eqk!#;$"2wmoV()eqk"!#<$"2wmoV()eqk"!#<-%*THICKNESSG6#""$-%'CURVESG6&7-7$$!#5!""$!"&!""7$$""!!""$"#5!""7$$"#5!""$"#D!""7$$"#?!""$"#S!""7$$"#I!""$"#b!""7$$"#S!""$"#q!""7$$"#]!""$"#&)!""7$$"#!)!""$"$D"!""7$$"#!*!""$"$X"!""7$$"$+"!""$"$g"!""7$$"$5"!""$"$v"!""-%&COLORG6&%$RGBG$"#5!""$""!!""$""!!""-%'SYMBOLG6$%*_SOLIDBOXG"#;-%&STYLEG6#%&POINTG-%%VIEWG6$;$!#5!""$"$5"!""%(DEFAULTG-&%&_AXISG6#"""6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#"""-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6%-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ(DEFAULT6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%%FONTG6%%(DEFAULTG%(DEFAULTG"#5-%%ROOTG6'-%)BOUNDS_XG6#$"$S"!""-%)BOUNDS_YG6#$"$I"!""-%-BOUNDS_WIDTHG6#$"%IP!""-%.BOUNDS_HEIGHTG6#$"%]N!""-%)CHILDRENG6"

subs(x=12.3,{line,pol,quad}); subs(x=12.3,1.0+1.5*x);

PCUkIitfNVVMPiEiKSQiK1pfcVQ+RiUkIis1KFJyIW9GJQ==

JCIlWD4hIiM=

Problem 11 pts:=[[1.02,-4.30], [1.00,-2.12], [0.99, 0.52], [1.03, 2.51], [1.00, 3.34], [1.02, 5.30]];

Nyg3JCQiJC0iISIjJCEkSSVGJjckJCIkKyJGJiQhJDcjRiY3JCQiIyoqRiYkIiNfRiY3JCQiJC4iRiYkIiReI0YmNyRGKiQiJE0kRiY3JEYkJCIkSSZGJg==

plot(pts,style=point,symbol=solidbox,symbolsize=16);

LSUlUExPVEc2Jy0lJ0NVUlZFU0c2JDcoNyQkIiQtIiEiIyQhI1YhIiI3JCQiIzUhIiIkISQ3IyEiIzckJCIjKiohIiMkIiNfISIjNyQkIiQuIiEiIyQiJF4jISIjNyQkIiM1ISIiJCIkTSQhIiM3JCQiJC0iISIjJCIjYCEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUrQVhFU0xBQkVMU0c2JFEhNiJRITYiLSUnU1lNQk9MRzYkJSpfU09MSURCT1hHIiM7LSUmU1RZTEVHNiMlJlBPSU5URy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJEklISIiLSUpQk9VTkRTX1lHNiMkIiRJIiEiIi0lLUJPVU5EU19XSURUSEc2IyQiJT9NISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJVNQISIiLSUpQ0hJTERSRU5HNiI=

E:=(m,b,data)->sum((m*data[i][1]+b-data[i][2])^2 , i=1..nops(data) );

Zio2JUkibUc2IkkiYkdGJUklZGF0YUdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkc3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQqJCwoKiY5JCIiIiYmOSY2I0kiaUdGJTYjRjVGNUY1OSVGNSZGNzYjIiIjISIiRj8vRjo7RjUtSSVub3BzR0YuNiNGOEYlRiVGJQ==

E(m,b,pts);

LC4qJCwoSSJtRzYiJCIkLSIhIiNJImJHRiYiIiIkIiRJJUYpRisiIiNGKyokLChGJSQiJCsiRilGKkYrJCIkNyNGKUYrRi5GKyokLChGJSQiIyoqRilGKkYrJCEjX0YpRitGLkYrKiQsKEYlJCIkLiJGKUYqRiskISReI0YpRitGLkYrKiQsKEYlRjFGKkYrJCEkTSRGKUYrRi5GKyokLChGJUYnRipGKyQhJEkmRilGK0YuRis=

solution:=solve({diff(E(m,b,pts),m),diff(E(m,b,pts),b)},{m,b});

PCQvSSJiRzYiJCErbm07eEkhIikvSSJtR0YlJCIrTExMTEpGKA==

line:=subs(solution,m*x+b);

LCZJInhHNiIkIitMTExMSiEiKSQhK25tO3hJRiciIiI=

with(plots): display(plot(pts,style=point,symbol=solidbox,symbolsize=16),plot(line, x=0..2,color=blue,thickness=3));

LSUlUExPVEc2KS0lJ0NVUlZFU0c2JjcoNyQkIiQtIiEiIyQhI1YhIiI3JCQiIzUhIiIkISQ3IyEiIzckJCIjKiohIiMkIiNfISIjNyQkIiQuIiEiIyQiJF4jISIjNyQkIiM1ISIiJCIkTSQhIiM3JCQiJC0iISIjJCIjYCEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUnU1lNQk9MRzYkJSpfU09MSURCT1hHIiM7LSUmU1RZTEVHNiMlJlBPSU5URy0lJ0NVUlZFU0c2JTdTNyQkIiIhISIiJCErbm07eEkhIik3JCQiMUxMTEwzVmZWISM8JCEybzNxdjtyMCVIISM6NyQkIjFubW0iSFtEOikhIzwkITEnRykpUTo/PCNHISM5NyQkIjJMTEwkZTAkPUMiISM8JCEya2hqKGUoZiEpbyMhIzo3JCQiMkxMTCQzUkJyOyEjPCQhMCR6eHZMXmBEISM4NyQkIjJsbW0iempmKTQjISM8JCEydlJrI29rZz5DISM6NyQkIjJLTExlNDtbXCMhIzwkITIkXD9zQndYJkgjISM6NyQkIjIoKioqKlxpJ3ldIUghIzwkITImcCw9J28zcDsjISM6NyQkIjFMTCRlenMkSEwhIzskITEsSzMiPmpSLiMhIzk3JCQiMiYqKioqXDdpSV9QISM8JCExeF0oUTBXOSE+ISM5NyQkIjFubW07X00oPSUhIzskITJBLSVlSz04bDwhIzo3JCQiMk1MTCQzeV9xWCEjPCQhMXRYKFEmejFYOyEjOTckJCIqbCs+KyYhIiokITJNMStOWS8qNDohIzo3JCQiKnZXXVYmISIqJCEyWiR5JSl5Zj11OCEjOjckJCIqTmZDJmUhIiokITIoWzwnMzInUlY3ISM6NyQkIjFMTCRlejY6QichIzskITJERjhYSUVZNyIhIzo3JCQiMW1tbTs9QyNvJyEjOyQhMCc9blljKFIkKSohIzk3JCQiMW1tbW0jcFMxKCEjOyQhMFpLLChIZVAnKSEjOTckJCIsRE9EIzN2ISM2JCExVUYrcVEqZUMoISM6NyQkIjFtbW1tKHk4IXohIzskITExXHUuSyw5ZyEjOjckJCIsRE9JRkwpISM2JCExdnZGcVtXaVkhIzo3JCQiLHYzek11KSEjNiQhMUZ5dSk+S2FQJCEjOjckJCIxbm1tIkhfPzwqISM7JCEyR3osRFxwRC4jISM7NyQkIjFubTt6aWhsJiohIzskITE6bCp6SkJTKnohIzs3JCQiMUxMTDMjRywqKiohIzskIjE2UzloL04yYCEjOzckJCIyS0wkZXp3NVY1ISM7JCIyQVRuTSZSUDc+ISM7NyQkIi12JFEjXCIzIiEjNiQiMik+XSpRbyU0OkohIzs3JCQiMktMTGUiKltINyIhIzskIjFXek9BZzE5VyEjOjckJCIqZHhkOyIhIikkIjEudVc+MC5jZCEjOjckJCIyKSoqKipcX3FuMjchIzskIjEsVyg0KDQpKW9xISM6NyQkIjIpKioqXGkmcEBbNyEjOyQiMEZSJClHSiJSJCkhIzk3JCQiMikqKioqXDInSEtIIiEjOyQiMWtELSVwRiZcKCohIzo3JCQiMmxtbW1adk9MIiEjOyQiMExXJWZKbyw2ISM4NyQkIit2KydvUCIhIiokIjIqelYoMyFcKnBCIiEjOjckJCIyS0wkZVI8KmZUIiEjOyQiMlE2KikpXHVnZjghIzo3JCQiKyYpSHhlOSEiKiQiMTQvPV9gbCRcIiEjOTckJCIybG07SCFvLSpcIiEjOyQiMTgjUjspUnk+OyEjOTckJCIyKioqKlw3ay42YSIhIzskIjIoKUhPPHVDO3YiISM6NyQkIjJtbW07V1RBZSIhIzskIjFUIkdJPUIwKT0hIzk3JCQiLUQxKjNgaSIhIzYkIjJvKltQMHpZOj8hIzo3JCQiMk1MTEwqenltOyEjOyQiMTpiYjZkVlhAISM5NyQkIjJMTEwzTjEjNDwhIzskIjJjUFRdY1kkeUEhIzo3JCQiMm1tO0hZdDd2IiEjOyQiMUpeYlxvOjVDISM5NyQkIip4RyoqeSIhIikkIjIvcE88Im9GSkQhIzo3JCQiMm1tbVQ2S1UkPSEjOyQiMXl1eGNSNHFFISM5NyQkIjJMTExMYmRRKD0hIzskIjFlSjptT0QleiMhIzk3JCQiLURPbDU7PiEjNiQiMSlINkUiUWpFSCEjOTckJCItdi5VYWM+ISM2JCIyJj15NC8mUUwwJCEjOjckJCIjPyEiIiQiKyoqKipcKj0kISIpLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIzUhIiItJSpUSElDS05FU1NHNiMiIiQtJSVWSUVXRzYkOyQiIiEhIiIkIiM/ISIiJShERUZBVUxURy0mJSZfQVhJU0c2IyIiIjYmLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiItJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSYlJl9BWElTRzYjIiIjNiYtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIi0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJStBWEVTTEFCRUxTRzYlLUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHNiI2NVEieDYiLyUnZmFtaWx5R1EoREVGQVVMVDYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2IlEhNiItJSVGT05URzYlJShERUZBVUxURyUoREVGQVVMVEciIzUtJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiQhXCEiIi0lKUJPVU5EU19ZRzYjJCIjISkhIiItJS1CT1VORFNfV0lEVEhHNiMkIiVJTSEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiVTUSEiIi0lKUNISUxEUkVORzYi