What is the extreme 2x^3+9x^2+12x+1 ?

The extreme 2x^3+9x^2+12x+1 is Maximum(-2,-3),Minimum(-1,-4)

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extreme 2x^3+9x^2+12x+1

extreme points

2 x^{3} + 9 x^{2} + 12 x + 1

Maximum (- 2, - 3), Minimum (- 1, - 4)

Solution steps

f^{'} (x) = 6 x^{2} + 18 x + 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < - 1,

Increasing

: - 1 < x < \infty

Plug

x = - 2

into

2 x^{3} + 9 x^{2} + 12 x + 1 : - 3

Maximum (- 2, - 3)

Plug

x = - 1

into

2 x^{3} + 9 x^{2} + 12 x + 1 : - 4

Minimum (- 1, - 4)

Maximum (- 2, - 3), Minimum (- 1, - 4)

f (x) = \frac{x ^{3}}{6} - \frac{5 x ^{2}}{4}

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

x^{5} - 10 x^{4} + 25 x^{3}

f (x, y) = x^{3} + y^{3} + 4 x y

f (x) = 6 x^{5} - 40 x^{3} + 45

What is the extreme 2x^3+9x^2+12x+1 ?
The extreme 2x^3+9x^2+12x+1 is Maximum(-2,-3),Minimum(-1,-4)