What is the extreme 2x^3-3x^2-12x+1 ?

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

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extreme 2x^3-3x^2-12x+1

extreme points

2 x^{3} - 3 x^{2} - 12 x + 1

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

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 + 1 : 8

Maximum (- 1, 8)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x + 1 : - 19

Minimum (2, - 19)

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

f (x) = 324 x - 72 x^{2} + 4 x^{3}

f (x) = 2 x + 3 y

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

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

y = e^{r x}

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