Calculus

Is it not .5 and .5? I'm confused.

Differentiating x(1-x) and setting the result to zero to look for extrema, the result is x = .5.

0.25

x + y = 1
x.y > 0

y = 1 - x

x.(1 - x) > 0 or x - x^2 > 0

Differentiate with respect to x to get turning points

f'(x) = 1 - 2x = 0 or 1 = 2x, x = 1/2

therefore y = 1 - 1/2 = 1/2 at the max point

Product = x.y = 1/2 * 1/2 = 1/4 or 0.25