What is the extreme f(x)=6-3x^2-x^3 ?

The extreme f(x)=6-3x^2-x^3 is Minimum(-2,2),Maximum(0,6)

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extreme f(x)=6-3x^2-x^3

extreme

Minimum (- 2, 2), Maximum (0, 6)

Solution steps

f^{'} (x) = - 3 x^{2} - 6 x

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

6 - 3 x^{2} - x^{3} : 2

Minimum (- 2, 2)

Plug

x = 0

into

6 - 3 x^{2} - x^{3} : 6

Maximum (0, 6)

Minimum (- 2, 2), Maximum (0, 6)

What is the extreme f(x)=6-3x^2-x^3 ?
The extreme f(x)=6-3x^2-x^3 is Minimum(-2,2),Maximum(0,6)