What is the extreme f(x)= 1/3 x^3-x ?

The extreme f(x)= 1/3 x^3-x is Maximum(-1, 2/3),Minimum(1,-2/3)

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extreme f(x)= 1/3 x^3-x

extreme points

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

Maximum (- 1, \frac{2}{3}), Minimum (1, - \frac{2}{3})

Solution steps

f^{'} (x) = x^{2} - 1

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

\frac{1}{3} x^{3} - x : \frac{2}{3}

Maximum (- 1, \frac{2}{3})

Plug

x = 1

into

\frac{1}{3} x^{3} - x : - \frac{2}{3}

Minimum (1, - \frac{2}{3})

Maximum (- 1, \frac{2}{3}), Minimum (1, - \frac{2}{3})

f (x, y) = - 3 x^{2} - 2 x y - 2 y^{2} + 400 x + 200 y

f (x, y) = 2 - 5 x^{2} - 2 y^{2}

f (x, y) = ln (9 - x^{2} - y^{2})

y = 4 - x^{2}

2 cos (x) + sin (2 x)

What is the extreme f(x)= 1/3 x^3-x ?
The extreme f(x)= 1/3 x^3-x is Maximum(-1, 2/3),Minimum(1,-2/3)