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

The extreme f(x)=2x^3+3x^2-12x-3 is Maximum(-2,17),Minimum(1,-10)

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

extreme points

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

Maximum (- 2, 17), Minimum (1, - 10)

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 - 3 : 17

Maximum (- 2, 17)

Plug

x = 1

into

2 x^{3} + 3 x^{2} - 12 x - 3 : - 10

Minimum (1, - 10)

Maximum (- 2, 17), Minimum (1, - 10)

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

f (x) = - 2 x^{4} - 24 x^{3} + 12

f (x) = 5 x^{2} + 4 x

f (x, y) = - \frac{1}{4} x^{4} + \frac{2}{3} x^{3} + 4 x y - y^{2}

f (x, y) = x y (10 - 2 x - 3 y)

What is the extreme f(x)=2x^3+3x^2-12x-3 ?
The extreme f(x)=2x^3+3x^2-12x-3 is Maximum(-2,17),Minimum(1,-10)