What is the extreme f(x)=4x^3+6x^2-24x ?

The extreme f(x)=4x^3+6x^2-24x is Maximum(-2,40),Minimum(1,-14)

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extreme f(x)=4x^3+6x^2-24x

extreme

Maximum (- 2, 40), Minimum (1, - 14)

Solution steps

f^{'} (x) = 12 x^{2} + 12 x - 24

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

4 x^{3} + 6 x^{2} - 24 x : 40

Maximum (- 2, 40)

Plug

x = 1

into

4 x^{3} + 6 x^{2} - 24 x : - 14

Minimum (1, - 14)

Maximum (- 2, 40), Minimum (1, - 14)

What is the extreme f(x)=4x^3+6x^2-24x ?
The extreme f(x)=4x^3+6x^2-24x is Maximum(-2,40),Minimum(1,-14)