Question

Find the absolute extremes of the function 𝑓(𝑥)=𝑥√(𝑥−𝑥^2)(provide answers as exact values).

Answer 1

y = x√(x-x^2)

y' = x(3-4x)/(2√(x-x^2))

since y is defined only on the interval [0,1]
min is at (0,0) and (1,0)
max is at (3/4, 3√3/16)