What is the extreme g(x)= 1/9 x^9-x ?

The extreme g(x)= 1/9 x^9-x is Maximum(-1, 8/9),Minimum(1,-8/9)

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extreme g(x)= 1/9 x^9-x

extreme points

g (x) = \frac{1}{9} x^{9} - x

Maximum (- 1, \frac{8}{9}), Minimum (1, - \frac{8}{9})

Solution steps

f^{'} (x) = x^{8} - 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{1}{9} x^{9} - x : \frac{8}{9}

Maximum (- 1, \frac{8}{9})

Plug

x = 1

into

\frac{1}{9} x^{9} - x : - \frac{8}{9}

Minimum (1, - \frac{8}{9})

Maximum (- 1, \frac{8}{9}), Minimum (1, - \frac{8}{9})

f (x, y) = x^{2} + y^{2} - 18 x + 12 y - 7

f (x) = x^{2} - 6 x + 6

f (x) = 2 x^{2} - 8 x + 11, 0 \leq x \leq 6

- 4 + 4 x + 2 x^{2}

f (x) = x^{\frac{3}{2}} (x - 5)

What is the extreme g(x)= 1/9 x^9-x ?
The extreme g(x)= 1/9 x^9-x is Maximum(-1, 8/9),Minimum(1,-8/9)