What is the extreme f(x)=x(x-4)^2 ?

The extreme f(x)=x(x-4)^2 is Maximum(4/3 , 256/27),Minimum(4,0)

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extreme f(x)=x(x-4)^2

extreme points

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

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

Solution steps

f^{'} (x) = (x - 4) (3 x - 4)

Find intervals:

Increasing

: - \infty < x < \frac{4}{3},

Decreasing

: \frac{4}{3} < x < 4,

Increasing

: 4 < x < \infty

Plug

x = \frac{4}{3}

into

x (x - 4)^{2} : \frac{256}{27}

Maximum (\frac{4}{3}, \frac{256}{27})

Plug

x = 4

into

x (x - 4)^{2} : 0

Minimum (4, 0)

Maximum (\frac{4}{3}, \frac{256}{27}), Minimum (4, 0)

What is the extreme f(x)=x(x-4)^2 ?
The extreme f(x)=x(x-4)^2 is Maximum(4/3 , 256/27),Minimum(4,0)