| Start | Um we have the midterm coming up in a week.
Do we all know where it is? Yes Harriman 137. That's the big room in Harriman. If you don't know where that room is you should find it between now and then. You know the exam is at 8:45 at night. So I'm almost done writing the exam. Then I'll come up with some practice stuff. There will be one more assignment sent. One more paper homework sent this week. I'll probably put it up tomorrow. For next week. And then next week you won't have one for the following week. |
| 0:35 | So the exam is Tuesday night 8:45 pm. That wasn't up to me.
They gave me the option of doing it in here but this isn't a good room to give an exam in. Um so yeah so we have a night exam. Um so far unless I change the exam it's 7 questions andI suspect that most of you will be able to do it in less than an hour. |
| 1:01 | But I can't promise that.
So don't make plans for 9:45. Okay? And we have to sign in everybody for the exam. So you don't get to leave just because you're finished. I didn't say it would take the whole time but we sign everybody in so you can't leave until we've signed everybody in. Also once anyone leaves nobody else is allowed to come in. So for those of you who seem to be incapable of arriving on time for exams if you arrive more than about a half an hour late you'r probably in trouble. |
| 1:36 | Okay? Because at some point that's it you can't come in.
So you should tell your friends who never come to class that they maybe want to come to class on time for that exam. You will be able to leave some of you might want to catch the train. There's like a 9:50 train or something. I will to my best to enable you to make it but it really depends on how smoothly everything is going. Okay? I have three TAs to help me. I think two of them actually. |
| 2:04 | There you go. So grading the exams that takes a day or two.
So you'll probably know how you did my Friday. Okay? I have no idea what the curve will be. Any questions? Yes? Tuesday. Tuesday night at 8:45. Did I say Monday? Okay, Tuesday night. I have a different midterm on Monday. This is also known as I have no life. Okay so when I get here I am missing Monday night football for you guys. |
| 2:33 | Just so you appreciate that.
Anyways um by the way why do they play the national anthem at football games? I mean why do we do that altogether? No one knows. No one can give me a good answer to that. Well not to get into a political discussion because I won't. I just find it fascinating. I mean who came up with that idea? And it seems to be a bad idea these days so there we go. How are we doing on all this derivative stuff? It's pretty easy right? |
| 3:00 | You're waiting for a catch. These are the easy derivatives.
As I said the hard part is doing something with the derivative. For example. |
| 3:43 | Let's see if you guys can do that.
|
| 7:46 | Alright that was long enough.
So let's do this one. Okay so it's the equation of the tangent line so you need to equation of a line. |
| 8:01 | The equation of a line is y-y1=m(x-x1) okay?
So that means you have y minus the y-coordinate is the slope times x minus the corresponding x-coordinate. So we have the x-coordinate which is 2. So we need to find two things. We need to find y1 which is the y-coordinate. We need to find the slope which we will do with calculus. And this is calculus class so you really only know how to do one thing so far. |
| 8:33 | So figure if you don't know what else, this is a typical exam question, if you don't know what else take the derivative.
So first let's find y1. To find y1 you plug in 2 for x, there you go. So now we're gonna have y- 5/2= m(x-2). Now let's find the slope. |
| 9:03 | Okay in order to find the slope we need to derivative. Because as I said this is calculus class.
The derivative of 5/x is -5/x^2 because that's one of those derivatives that we memorize. Okay remember? The derivative of 1/x is -1/x^2. |
| 9:31 | So the derivative of 5/x is -5/x^2.
So far so good? Okay then you plug it in. You get y-5- oops sorry. Now we have to evaluate this at x=2. Which should give you -5/4. Therefore the tangent line is y- 5/2= -5/4(x-2). |
| 10:04 | And yes you can leave it like that during the exam.
You don't need to put it in another form. There's no right form for lines. So you can leave it exactly like that okay? How'd we do on that one? Let's do another one. |
| 10:57 | Okay same procedure. There you go.
|
| 15:11 | How are we doing on this? Are we back to checking our twitter feed?
Well let's go through it. |
| 15:31 | Okay lot's of buzzing so that's a good sign.
So just like last time, now sometimes I might actually give you the y-coordinate. But these are easy to find the y-coordinate. The same as before. Say look, you have the equation of a line. So I'm going to need to find two things. Two pieces of information. You're going to need to find y1 and you need to find the slope. So first let's find y1. |
| 16:05 | To find y1 this equation gives me y so I want to find y. Remember y1 just stands for a particular y.
So I plug in 1 and I get 1^3 + 4(1) -2 = 3. Everybody happy with that? So that means we've now found half of this information. |
| 16:31 | Okay? We've got that much of the equation of the line. We're just missing the slope.
Now we can find the slope. The slope is the derivative. So dy/dx = 3x^2 +4. Were you all capable of doing the derivative? You have any troubles finding the derivative of that? Okay but we have to evaluate it at x=1. |
| 17:01 | You can't just sort of leave it like this.
Remember the derivative gives us the slope at any random point x. Now we want to find it at a specific point, x=1. So at x=1 this equals 3+4=7. So the equation is y-3=7(x-1). We good? |
| 17:30 | So I would expect to see something like this so let's practice one more.
Make sure everybody's got the idea. Now I could mess with you and give you a pi but that would be mean. |
| 18:14 | That one is slightly harder.
I don't know. I don't know if we'll have videos up before the test. I will have a practice sheet for you guys tomorrow. |
| 18:36 | Once I confer with the TAs as to what exactly is on the exam.
Then we'll put up a practice set. Remember the videos were not designed for this course. The videos were designed for future courses. |
| 19:03 | So if I can find a way to get ahold of the videos now I'll put them up.
They weren't really intended for this semester. |
| 24:23 | I'll give you guys about 30 more seconds.
|
| 24:32 | I can make it harder.
Alright that's long enough. So the question you're asking yourself is how do I take the derivative of 1/√ x? So this is what we can do to you. When we say we I mean me. So first let's find our y-coordinate. So y is going to be √ 16 +1/√ 16 which is 4+1/4 also known as 17/4. |
| 25:01 | You really shouldn't do that 4+1/4 thing you guys are too old for that.
So far so good? So we found- now we're going to have y- 17/4= m(x-16). Okay did you all get 4 and 1/4? 4.25? 17/4? Did everyone get some variation of that? Good. Derivative. Well this, you could rewrite this. |
| 25:37 | As x^1/2 - x^-1/2.
So we memorize the derivative of √ x. That's 1/2√ x. Or if you wanted you could've done the derivative of x^1/2 is 1/2x^-1/2. |
| 26:03 | And that can be rewritten as 1/2√ x.
So you can do it either way. Okay? That's why I recommend memorizing this one and memorizing the 1/x. It just simplifies your life. Because I'll throw a bunch of these in for the rest of the semester. What about x^-1/2. Well bring the -1/2 in front, x^-3/2. Some of you even got to that step and said yeah but I don't know what x^-3/2 is. |
| 26:32 | Which, okay we'll let that slide.
And now you want to evaluate this at x=16. Well when you take the √ 16 that's 4. So what do we do about 16^-3/2? Because that means 1/16^ 3/2. And do you remember what 16^3/2 means? It means you take the square root of 16 and then you cube it. |
| 27:04 | Or you could cube it first and then take the square root but that's more work.
So that's what the 3/2 means the √ 16 is 4, 4^3 is 64. So this then becomes 1/2*4 - 1/2*64. |
| 27:40 | So far so good?
That's 15/128. Among other things. Okay? Which you wouldn't have to reduce. If you're really desperate you could leave it as some version of this. You won't get full credit but you'll get almost full credit. |
| 28:04 | Because if you go here and you say look I got everything right I just don't know how to find 16^3/2 we'll take off a point or two.
You won't get to stay in college you'll have to go back home and live in the garage. Living the rest of your life ruined by one exam question. Now when you plug in you get y- 17/4= 15/128(x-16). |
| 28:35 | How'd we do on this one?
Yes? Question- For the x^-/12 can't you do instead of that you write 1/1/2√ x? Uh no it's not the same thing. Yeah is it the same thing as 1/1/2√ x? No. So no when you take the derivatives you're going to want to convert these into their fractional exponents. |
| 29:02 | Positive or negative then you're going to want to take the derivative.
Alright so if you have y equals the cube root of x and you want to do the derivative of the cube root of x You want to do the derivative of the cube root of x you'd want to do the derivative of x^1/3. Which is 1/3x^-2/3. |
| 29:31 | So if you were doing the derivative of 1 over the cube root of x
that would be the derivative of x^-1/3.
Which is -1/3x^-4/3. What's x^-4/3? I don't know if you can read my handwriting that's a 4/3. |
| 30:09 | That's 1 over cube root of x to the forth.
I'll try not to give you any messy fractions on the exam. It's not a fractions test. But as I said if you get to the point where you say look I can do this but the arithmetic is messy and I'm a calculator person because this is the year 2017 I understand and um don't simplify it then. |
| 30:34 | Okay? You have my sympathy about the calculators.
I said why can't we let students use calculators in 122 after all you're not moving on. It's not as if you're going to be crippled by the lack of calculator. And I was told you could use them to cheat. What was my response? Pretty much you'll find another way to cheat if you don't use your calculator. Right? Haters gonna hate. Cheaters gonna cheat. |
| 31:00 | So you know that really wasn't an issue to me.
But that could be one way to cheat. But some of you that's just who you are. It's not going to change just because we take your calculator away. Okay um we recommend that you don't do that. If we catch you it tends to be bad. But you know some of you insist. How do we feel about these tangent line problems? Do we feel good? You want one more just to make sure? One more? Okay we'll give you one more. |
| 31:44 | What makes you think these aren't the kind that will be on the test?
Well it could look like that. It could look like that it could look easier. I'll give you one more that I'd consider sort of a- I'm sorry? |
| 32:05 | Okay I mean I consider all of these relatively the same level.
That's me. Are you guys complaining right now? Is that what you're doing? I mean you're allowed to complain. I would say I would make sure you could do something like... |
| 32:48 | Let's see if you could do something like that.
|
| 38:07 | Alright let's do this one.
So as always we need the y-coordinate. y=5(2^3)- 4(2^2) -8. Other than the exam you could use a calculator but you should practice doing these without a calculator. |
| 38:30 | And you should get 16.
Is that what you guys got? Okay good. Now we need the derivative. The derivative is 16x^2 -8x -0. And you do that at x=2 and you get 15(4) -8(4) is 28. So far so good? |
| 39:01 | 8 times 2, whoops my bad.
Is uh 44. How'd we do on that? Okay so y-16= 44(x-2) How'd we do on this? |
| 39:30 | Feeling good about that?
Okay so you'll get one of these types will be on the exam but I'm not going to promise which type. Okay so Friday we're going to do some exam review. So maybe those of you who don't come will come. We'll see. Everybody have a nice day we'll see you on Friday. |