What is the extreme f(x)=-x^3+27x-54 ?

The extreme f(x)=-x^3+27x-54 is Minimum(-3,-108),Maximum(3,0)

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extreme f(x)=-x^3+27x-54

extreme

Minimum (- 3, - 108), Maximum (3, 0)

Solution steps

f^{'} (x) = - 3 x^{2} + 27

Find intervals:

Decreasing

: - \infty < x < - 3,

Increasing

: - 3 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 3

into

- x^{3} + 27 x - 54 : - 108

Minimum (- 3, - 108)

Plug

x = 3

into

- x^{3} + 27 x - 54 : 0

Maximum (3, 0)

Minimum (- 3, - 108), Maximum (3, 0)

What is the extreme f(x)=-x^3+27x-54 ?
The extreme f(x)=-x^3+27x-54 is Minimum(-3,-108),Maximum(3,0)