00:01
Find the maximum value of f of x equals x times a times a to x times b on the interval 0 is less than x is less than or equal to 8 given that a and b are positive numbers.
00:11
First of all, we could rewrite f of x.
00:14
We multiply 8 times a times b.
00:17
Just get that constant part out of the way.
00:20
And then we multiply x times x and that gives us x squared.
00:24
So again, 8 a b, that will be a constant since a and b are given to be positive numbers.
00:29
So let's find the derivative of that function, f prime of x, that would just be this constant of 8 a b times the derivative of x squared, which is 2x.
00:40
And we could simplify that to 16ab times x.
00:45
And that's just over the interval, 0 is less than x is less than or equal to 8...