What is the extreme 2x^3-3x^2-12x ?

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

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extreme 2x^3-3x^2-12x

extreme points

2 x^{3} - 3 x^{2} - 12 x

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

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

Maximum (- 1, 7)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x : - 20

Minimum (2, - 20)

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

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

f (x, y) = 4 x y - x^{2} y - x y^{2}

f (x) = \frac{1}{4} x^{4} - 2 x^{2}

f (x) = x^{3} (x - 5)^{2}

f (x) = 1 + 3 x^{2} - 2 x^{3}

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