What is the extreme f(x)=x^4(1-x)^8 ?

The extreme f(x)=x^4(1-x)^8 is Minimum(0,0),Maximum(1/3 , 256/531441),Minimum(1,0)

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extreme f(x)=x^4(1-x)^8

extreme

Minimum (0, 0), Maximum (\frac{1}{3}, \frac{256}{531441}), Minimum (1, 0)

Solution steps

f^{'} (x) = 4 x^{3} (x - 1)^{7} (3 x - 1)

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Increasing

: 1 < x < \infty

Plug

x = 0

into

x^{4} (1 - x)^{8} : 0

Minimum (0, 0)

Plug

x = \frac{1}{3}

into

x^{4} (1 - x)^{8} : \frac{256}{531441}

Maximum (\frac{1}{3}, \frac{256}{531441})

Plug

x = 1

into

x^{4} (1 - x)^{8} : 0

Minimum (1, 0)

Minimum (0, 0), Maximum (\frac{1}{3}, \frac{256}{531441}), Minimum (1, 0)

What is the extreme f(x)=x^4(1-x)^8 ?
The extreme f(x)=x^4(1-x)^8 is Minimum(0,0),Maximum(1/3 , 256/531441),Minimum(1,0)