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

The extreme f(x)=-x^3+3x-3 is Minimum(-1,-5),Maximum(1,-1)

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extreme f(x)=-x^3+3x-3

extreme points

f (x) = - x^{3} + 3 x - 3

Minimum (- 1, - 5), Maximum (1, - 1)

Solution steps

f^{'} (x) = - 3 x^{2} + 3

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

- x^{3} + 3 x - 3 : - 5

Minimum (- 1, - 5)

Plug

x = 1

into

- x^{3} + 3 x - 3 : - 1

Maximum (1, - 1)

Minimum (- 1, - 5), Maximum (1, - 1)

f (x) = - x^{3} + 3 x^{2} + 24 x - 4

x^{2} + 4 x + 4

f (x) = \frac{x ^{2}}{ln ( x )}

f (x, y) = x^{6} + x y - 2 y - x + 3

f (x) = 3 cos^{2} (x)

What is the extreme f(x)=-x^3+3x-3 ?
The extreme f(x)=-x^3+3x-3 is Minimum(-1,-5),Maximum(1,-1)