What is the extreme f(x)=-x^3+3x+2 ?

The extreme f(x)=-x^3+3x+2 is Minimum(-1,0),Maximum(1,4)

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extreme f(x)=-x^3+3x+2

extreme points

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

Minimum (- 1, 0), Maximum (1, 4)

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 + 2 : 0

Minimum (- 1, 0)

Plug

x = 1

into

- x^{3} + 3 x + 2 : 4

Maximum (1, 4)

Minimum (- 1, 0), Maximum (1, 4)

What is the extreme f(x)=-x^3+3x+2 ?
The extreme f(x)=-x^3+3x+2 is Minimum(-1,0),Maximum(1,4)