What is the extreme f(x)=-6x^3+18x^2+54x-72 ?

The extreme f(x)=-6x^3+18x^2+54x-72 is Minimum(-1,-102),Maximum(3,90)

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extreme f(x)=-6x^3+18x^2+54x-72

extreme

Minimum (- 1, - 102), Maximum (3, 90)

Solution steps

f^{'} (x) = - 18 x^{2} + 36 x + 54

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 3,

Decreasing

: 3 < x < \infty

Plug

x = - 1

into

- 6 x^{3} + 18 x^{2} + 54 x - 72 : - 102

Minimum (- 1, - 102)

Plug

x = 3

into

- 6 x^{3} + 18 x^{2} + 54 x - 72 : 90

Maximum (3, 90)

Minimum (- 1, - 102), Maximum (3, 90)

What is the extreme f(x)=-6x^3+18x^2+54x-72 ?
The extreme f(x)=-6x^3+18x^2+54x-72 is Minimum(-1,-102),Maximum(3,90)