What is the extreme f(x)=2x^3-3x^2-12x-7 ?

The extreme f(x)=2x^3-3x^2-12x-7 is Maximum(-1,0),Minimum(2,-27)

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extreme f(x)=2x^3-3x^2-12x-7

extreme points

f (x) = 2 x^{3} - 3 x^{2} - 12 x - 7

Maximum (- 1, 0), Minimum (2, - 27)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

2 x^{3} - 3 x^{2} - 12 x - 7 : 0

Maximum (- 1, 0)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x - 7 : - 27

Minimum (2, - 27)

Maximum (- 1, 0), Minimum (2, - 27)

What is the extreme f(x)=2x^3-3x^2-12x-7 ?
The extreme f(x)=2x^3-3x^2-12x-7 is Maximum(-1,0),Minimum(2,-27)