00:01
Okay, so we have, we're trying to maximize a rectangle inside of a semicircle given by this equation here.
00:07
So by this equation, we're given that y is equal to the square root of 25 minus x squared.
00:12
So we can plug that into our area equation to get x times 25 minus x squared.
00:22
So now what we want to do here is we want to find the derivative of our area equation.
00:27
And we can do that by using a product rule.
00:29
Product rule is we keep one the same, change the other, then add, change the other, and keep one the same.
00:36
Or just do the opposite.
00:38
So the first time around, we're going to do the derivative of x, which we should get one, and then keep the second function the same.
00:47
You have a square root of 25 minus x.
00:50
And then we're going to add doing the opposite.
00:53
So we're going to keep x the same, and then we're going to do the derivative of a square root of 25 minus x squared.
01:03
So this is going to be a chain rule here...