If a and b are positive numbers, find the maximum value of f(x) = x^a(1 - x)^b on the interval 0 ≤ x ≤ 1.?
f'(x) = x^a . -b(1-x)^(b-1) + (1-x)^b . ax^(a-1)
The Attempt at a Solution
I know to set f'(x) = 0 but i'm not sure how i'm supposed to tidy up the f'(x) above..