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

The extreme 2x^3+3x^2-12x+1 is Maximum(-2,21),Minimum(1,-6)

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

extreme points

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

Maximum (- 2, 21), Minimum (1, - 6)

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 + 1 : 21

Maximum (- 2, 21)

Plug

x = 1

into

2 x^{3} + 3 x^{2} - 12 x + 1 : - 6

Minimum (1, - 6)

Maximum (- 2, 21), Minimum (1, - 6)

f (x) = 8 x - x^{4}

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

f (x) = - x^{2} - 6 x + 9

f (x) = - x^{2} - 6 x - 8

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

What is the extreme 2x^3+3x^2-12x+1 ?
The extreme 2x^3+3x^2-12x+1 is Maximum(-2,21),Minimum(1,-6)