What is the extreme f(x)=x(1-x)^4 ?

The extreme f(x)=x(1-x)^4 is Maximum(1/5 , 256/3125),Minimum(1,0)

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extreme f(x)=x(1-x)^4

extreme points

f (x) = x (1 - x)^{4}

Maximum (\frac{1}{5}, \frac{256}{3125}), Minimum (1, 0)

Solution steps

f^{'} (x) = (x - 1)^{3} (5 x - 1)

Find intervals:

Increasing

: - \infty < x < \frac{1}{5},

Decreasing

: \frac{1}{5} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{5}

into

x (1 - x)^{4} : \frac{256}{3125}

Maximum (\frac{1}{5}, \frac{256}{3125})

Plug

x = 1

into

x (1 - x)^{4} : 0

Minimum (1, 0)

Maximum (\frac{1}{5}, \frac{256}{3125}), Minimum (1, 0)

What is the extreme f(x)=x(1-x)^4 ?
The extreme f(x)=x(1-x)^4 is Maximum(1/5 , 256/3125),Minimum(1,0)