найдите наибольшие и наименьшие значение функции y=x * (x-1) ^2

f (y) = x (x - 1) ^2

f' (x) = x' (x - 1) ^2 + (x - 1) ^2'x

f' (x) = (x - 1) ^2 + 2x (x - 1)

f' (x) = x^2 - 2x + 1 + 2x^2 - 2x

f' (x) = 3x^2 - 4x + 1

f' (x) = 0

3x^2 - 4x + 1 = 0

x1 = 1, x2 = 1/3

f (1) = 1 (1-1) ^2 = 0

f (1/3) = 1/3 (1/3 - 1) ^2 = 1/3 * (-4/9) = - 4/27

ymax = 0

ymin = - 4/27