00:01
Since there's a lot going on, i'm just going to jump right into answering a few of these questions.
00:11
Like on letter a, when they ask you to do g of 2, you have to plug in 2 for that at x.
00:18
So, 2 times 2 is 4.
00:20
And what you really need to do now is that we're doing area under the curve.
00:24
So if i'm looking at from 0 to 4, doing that area, you first have a triangle whose area is 1 half.
00:33
Then you have a semicircle with a radius of 1.
00:38
I should probably write out r equals 1.
00:40
And then from 3 to 4 is another 1 half.
00:45
So adding the halves together, 1 half plus 1 half would be 1.
00:49
And then pi r squared, so pi times 1 squared is 1, divided by 2 because it's only half of a circle.
00:57
And it's below the x -axis, so it should actually be negative.
01:00
I guess i should mention that being below the x -axis is a negative area.
01:05
Pi 1 squared over 2.
01:09
Okay, so looking at the next one, in letter a, they want you to do the derivative of 2.
01:16
Well, the first thing i would point out is that g prime will cancel out the derivative, except it's the chain rule.
01:22
So it's going to be f of 2x times the derivative of 2x, which is 2.
01:27
So what you really have to do when you do g prime of 2 is you need to know what f of 4 is, and then multiply by 2.
01:38
So if you look closely at f of 4, you get an answer of 1, and then multiply by 2 and you get 2.
01:47
So the next one is local mins and maxes for g.
01:54
And it's rooted in this equation.
01:57
So i'm doing letter b, because if you have a local min or a local max, the derivative needs to equal 0.
02:09
And so what we're really looking at is where 2f of 2x will equal 0.
02:15
So that'll only happen as if f of 2x equals 0...