What is the extreme f(x)=2x^3+6x^2-48x ?

The extreme f(x)=2x^3+6x^2-48x is Maximum(-4,160),Minimum(2,-56)

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extreme f(x)=2x^3+6x^2-48x

extreme

Maximum (- 4, 160), Minimum (2, - 56)

Solution steps

f^{'} (x) = 6 x^{2} + 12 x - 48

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 4

into

2 x^{3} + 6 x^{2} - 48 x : 160

Maximum (- 4, 160)

Plug

x = 2

into

2 x^{3} + 6 x^{2} - 48 x : - 56

Minimum (2, - 56)

Maximum (- 4, 160), Minimum (2, - 56)

What is the extreme f(x)=2x^3+6x^2-48x ?
The extreme f(x)=2x^3+6x^2-48x is Maximum(-4,160),Minimum(2,-56)