What is the extreme f(x)=12+6x^2-x^3 ?

The extreme f(x)=12+6x^2-x^3 is Minimum(0,12),Maximum(4,44)

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extreme f(x)=12+6x^2-x^3

extreme

Minimum (0, 12), Maximum (4, 44)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

12 + 6 x^{2} - x^{3} : 12

Minimum (0, 12)

Plug

x = 4

into

12 + 6 x^{2} - x^{3} : 44

Maximum (4, 44)

Minimum (0, 12), Maximum (4, 44)

What is the extreme f(x)=12+6x^2-x^3 ?
The extreme f(x)=12+6x^2-x^3 is Minimum(0,12),Maximum(4,44)