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## Homework Statement

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.?

## Homework Equations

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..