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

The extreme f(x)=2x^3+3x^2-12x+2 is Maximum(-2,22),Minimum(1,-5)

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

extreme points

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

Maximum (- 2, 22), Minimum (1, - 5)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

2 x^{3} + 3 x^{2} - 12 x + 2 : 22

Maximum (- 2, 22)

Plug

x = 1

into

2 x^{3} + 3 x^{2} - 12 x + 2 : - 5

Minimum (1, - 5)

Maximum (- 2, 22), Minimum (1, - 5)

What is the extreme f(x)=2x^3+3x^2-12x+2 ?
The extreme f(x)=2x^3+3x^2-12x+2 is Maximum(-2,22),Minimum(1,-5)