What is the extreme f(x)=-3x^3+27x ?

The extreme f(x)=-3x^3+27x is Minimum(-sqrt(3),-18sqrt(3)),Maximum(sqrt(3),18sqrt(3))

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extreme f(x)=-3x^3+27x

extreme

Minimum (- 3, - 183), Maximum (3, 183)

Solution steps

f^{'} (x) = - 9 x^{2} + 27

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- 3 x^{3} + 27 x : - 183

Minimum (- 3, - 183)

Plug

x = 3

into

- 3 x^{3} + 27 x : 183

Maximum (3, 183)

Minimum (- 3, - 183), Maximum (3, 183)

What is the extreme f(x)=-3x^3+27x ?
The extreme f(x)=-3x^3+27x is Minimum(-sqrt(3),-18sqrt(3)),Maximum(sqrt(3),18sqrt(3))