What is the extreme f(x)=x(x-1)^5 ?

The extreme f(x)=x(x-1)^5 is Minimum(1/6 ,-3125/46656),Saddle(1,0)

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extreme f(x)=x(x-1)^5

extreme points

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

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Saddle (1, 0)

Solution steps

f^{'} (x) = (x - 1)^{4} (6 x - 1)

Find intervals:

Decreasing

: - \infty < x < \frac{1}{6},

Increasing

: \frac{1}{6} < x < 1,

Increasing

: 1 < x < \infty

Plug

x = \frac{1}{6}

into

x (x - 1)^{5} : - \frac{3125}{46656}

Minimum (\frac{1}{6}, - \frac{3125}{46656})

Plug

x = 1

into

x (x - 1)^{5} : 0

Saddle (1, 0)

Minimum (\frac{1}{6}, - \frac{3125}{46656}), Saddle (1, 0)

2 x^{2} - 30 x^{2} + 54 x + 2

y = (x - 6) ln (x - 6)

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

p (x) = 12 x^{4} - 62 x^{3} + a x^{2} - 98 x + 30

y = 3 z^{2} - 3 x^{2}

What is the extreme f(x)=x(x-1)^5 ?
The extreme f(x)=x(x-1)^5 is Minimum(1/6 ,-3125/46656),Saddle(1,0)