What is the extreme 2x^3-3x^2-12x+5 ?

The extreme 2x^3-3x^2-12x+5 is Maximum(-1,12),Minimum(2,-15)

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extreme 2x^3-3x^2-12x+5

extreme points

2 x^{3} - 3 x^{2} - 12 x + 5

Maximum (- 1, 12), Minimum (2, - 15)

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 + 5 : 12

Maximum (- 1, 12)

Plug

x = 2

into

2 x^{3} - 3 x^{2} - 12 x + 5 : - 15

Minimum (2, - 15)

Maximum (- 1, 12), Minimum (2, - 15)

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

\frac{x}{x ^{2} + 10 x + 21}

f (x) = x^{3} + 15 x^{2} - 33 x

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

f (x) = - \frac{1}{2} x^{4} + 2 x^{3} + 28 x^{2} + 18

What is the extreme 2x^3-3x^2-12x+5 ?
The extreme 2x^3-3x^2-12x+5 is Maximum(-1,12),Minimum(2,-15)