Question

If a and b are positive numbers, find the maximum value of f(x) = x^a (1-x)^b , where 0<= x <= 1

Answer 1

You need to critical numbers.

Answer 2

do you know how to find the critical numbers?

Answer 3

Anyways, you can check f''(x) at x=a/(a+b). It'll turn out to be negative.