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

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

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

extreme points

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

Minimum (- 1, - 3), 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 - 1 : - 3

Minimum (- 1, - 3)

Plug

x = 1

into

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

Maximum (1, 1)

Minimum (- 1, - 3), Maximum (1, 1)

x^{3} - 9 x + 2

f (x) = 2 x^{3} - 9 x^{2} - 60 x + 8

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

f (x, y) = 7 e^{y} - 7 y e^{x}

f (x) = x^{4} - 50 x^{2} + 3

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