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

The extreme f(x)=2x^3+3x^2-12x is Maximum(-2,20),Minimum(1,-7)

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

extreme points

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

Maximum (- 2, 20), Minimum (1, - 7)

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 : 20

Maximum (- 2, 20)

Plug

x = 1

into

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

Minimum (1, - 7)

Maximum (- 2, 20), Minimum (1, - 7)

f (x) = - x^{2} + 10 x - 23

f (x) = \frac{x + 3}{x + 6}

5 sin (3 x + π)

f (x) = - 16 t^{2} + 1700

f (x) = \frac{6 x}{x ^{2} + 16}

What is the extreme f(x)=2x^3+3x^2-12x ?
The extreme f(x)=2x^3+3x^2-12x is Maximum(-2,20),Minimum(1,-7)