What is the extreme f(x)=-x^3+27x-49 ?

The extreme f(x)=-x^3+27x-49 is Minimum(-3,-103),Maximum(3,5)

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extreme f(x)=-x^3+27x-49

extreme

Minimum (- 3, - 103), Maximum (3, 5)

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 - 49 : - 103

Minimum (- 3, - 103)

Plug

x = 3

into

- x^{3} + 27 x - 49 : 5

Maximum (3, 5)

Minimum (- 3, - 103), Maximum (3, 5)

What is the extreme f(x)=-x^3+27x-49 ?
The extreme f(x)=-x^3+27x-49 is Minimum(-3,-103),Maximum(3,5)