What is the extreme f(x)=-1/2 x^3+3/2 x-1 ?

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

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extreme f(x)=-1/2 x^3+3/2 x-1

extreme points

f (x) = - \frac{1}{2} x^{3} + \frac{3}{2} x - 1

Minimum (- 1, - 2), Maximum (1, 0)

Solution steps

f^{'} (x) = - \frac{3}{2} (x + 1) (x - 1)

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - 1

into

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

Minimum (- 1, - 2)

Plug

x = 1

into

- \frac{1}{2} x^{3} + \frac{3}{2} x - 1 : 0

Maximum (1, 0)

Minimum (- 1, - 2), Maximum (1, 0)

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