What is the extreme g(x)=-x^3+3x-10 ?

The extreme g(x)=-x^3+3x-10 is Minimum(-1,-12),Maximum(1,-8)

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extreme g(x)=-x^3+3x-10

extreme points

g (x) = - x^{3} + 3 x - 10

Minimum (- 1, - 12), Maximum (1, - 8)

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 - 10 : - 12

Minimum (- 1, - 12)

Plug

x = 1

into

- x^{3} + 3 x - 10 : - 8

Maximum (1, - 8)

Minimum (- 1, - 12), Maximum (1, - 8)

f (x) = \frac{1}{20} x^{2} - 25 x

f (x) = 3 x^{3} + \frac{9}{2} x^{2} - 54 x + 1

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

f (x) = \frac{x ^{4} - 5 x + 7}{x ^{2} + 1}

f (x) = 5 - 6 x^{2}

What is the extreme g(x)=-x^3+3x-10 ?
The extreme g(x)=-x^3+3x-10 is Minimum(-1,-12),Maximum(1,-8)