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

The extreme 2x^3-3x^2-12x+12 is Maximum(-1,19),Minimum(2,-8)

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

extreme points

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

Maximum (- 1, 19), Minimum (2, - 8)

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 + 12 : 19

Maximum (- 1, 19)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x + 12 : - 8

Minimum (2, - 8)

Maximum (- 1, 19), Minimum (2, - 8)

f (x) = x^{3} - 3 x + 1, 0 \leq x \leq 5

f (x) = cos (7 x)

f (x) = x - 2 ln (x)

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

f (x) = 12 + 2 x - x^{2}, 0 \leq x \leq 5

What is the extreme 2x^3-3x^2-12x+12 ?
The extreme 2x^3-3x^2-12x+12 is Maximum(-1,19),Minimum(2,-8)