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

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

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

extreme points

y = 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)

y = \frac{e ^{(2 - x)} + x ^{2} - x}{2}

f (x) = 20 (1 + \frac{1}{x} + \frac{1}{x ^{2}})

2 x^{2} - 2 x y + y^{2} - 2 x

f (x) = \frac{y - 1}{y ^{3} - y + 1}

f (x, y) = 2 x^{2} + 2 y^{2} - 16 x + 12 y

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