What is the extreme g(x)=x(x-1)^2 ?

The extreme g(x)=x(x-1)^2 is Maximum(1/3 , 4/27),Minimum(1,0)

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extreme g(x)=x(x-1)^2

extreme points

g (x) = x (x - 1)^{2}

Maximum (\frac{1}{3}, \frac{4}{27}), Minimum (1, 0)

Solution steps

f^{'} (x) = (x - 1) (3 x - 1)

Find intervals:

Increasing

: - \infty < x < \frac{1}{3},

Decreasing

: \frac{1}{3} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{3}

into

x (x - 1)^{2} : \frac{4}{27}

Maximum (\frac{1}{3}, \frac{4}{27})

Plug

x = 1

into

x (x - 1)^{2} : 0

Minimum (1, 0)

Maximum (\frac{1}{3}, \frac{4}{27}), Minimum (1, 0)

y = x^{3} - 12 x

f (x) = t^{3} - 13 t^{2} + 50 t - 56

f (x) = x^{2} + 3 x - 3

f (x) = x^{4} - 4 x^{2} = x^{2} (x^{2} - 4)

f (x) = x y - x^{2} y - x y^{2}

What is the extreme g(x)=x(x-1)^2 ?
The extreme g(x)=x(x-1)^2 is Maximum(1/3 , 4/27),Minimum(1,0)