What is the extreme f(x)=1+12x-x^3 ?

The extreme f(x)=1+12x-x^3 is Minimum(-2,-15),Maximum(2,17)

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extreme f(x)=1+12x-x^3

extreme

Minimum (- 2, - 15), Maximum (2, 17)

Solution steps

f^{'} (x) = - 3 x^{2} + 12

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

1 + 12 x - x^{3} : - 15

Minimum (- 2, - 15)

Plug

x = 2

into

1 + 12 x - x^{3} : 17

Maximum (2, 17)

Minimum (- 2, - 15), Maximum (2, 17)

What is the extreme f(x)=1+12x-x^3 ?
The extreme f(x)=1+12x-x^3 is Minimum(-2,-15),Maximum(2,17)