What is the extreme f(x)=-2x^3+12x ?

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

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extreme f(x)=-2x^3+12x

extreme

Minimum (- 2, - 82), Maximum (2, 82)

Solution steps

f^{'} (x) = - 6 x^{2} + 12

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

- 2 x^{3} + 12 x : - 82

Minimum (- 2, - 82)

Plug

x = 2

into

- 2 x^{3} + 12 x : 82

Maximum (2, 82)

Minimum (- 2, - 82), Maximum (2, 82)

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