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

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)

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)