Question

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

Answer 1

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