00:01
Here we're given a function and we want to find the absolute max and min on an interval.
00:04
So we'll start off by saying f of x is equal to x squared times the square root of 6 minus x.
00:08
And we only care from 0 to 6.
00:11
So let's take the derivative.
00:13
That's going to be a product rule.
00:14
So we have the derivative of the first, that's 2x, times the second, plus the derivative of the second, which is going to be one half of this 6 minus x to the negative one half times negative 1 times the first, that's x squared.
00:30
And we'll set that equal to 0.
00:32
So when we want to set this equal to 0, let's go ahead and simplify by, let's multiply by the square root of 6x, and factor out x as well.
00:41
So i have 6 times 6 minus x times 2.
00:46
And then over here we have minus, we have, let's see, the 6 minus one half x squared, so x squared over 2...