What is the extreme f(x)=-x^3+12x-24 ?

The extreme f(x)=-x^3+12x-24 is Minimum(-2,-40),Maximum(2,-8)

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extreme f(x)=-x^3+12x-24

extreme points

f (x) = - x^{3} + 12 x - 24

Minimum (- 2, - 40), Maximum (2, - 8)

Solution steps

f^{'} (x) = - 3 x^{2} + 12

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- x^{3} + 12 x - 24 : - 40

Minimum (- 2, - 40)

Plug

x = 2

into

- x^{3} + 12 x - 24 : - 8

Maximum (2, - 8)

Minimum (- 2, - 40), Maximum (2, - 8)

f (x) = x^{2} - 4 x + 16

f (x) = - x^{3} + 12 x - 15

y = - 4 x^{3} - 18 x^{2} + 216 x - 12

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

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

What is the extreme f(x)=-x^3+12x-24 ?
The extreme f(x)=-x^3+12x-24 is Minimum(-2,-40),Maximum(2,-8)