What is the extreme f(x)=(2x^3)/3-x^2-12x ?

The extreme f(x)=(2x^3)/3-x^2-12x is Maximum(-2, 44/3),Minimum(3,-27)

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extreme f(x)=(2x^3)/3-x^2-12x

extreme points

f (x) = \frac{2 x ^{3}}{3} - x^{2} - 12 x

Maximum (- 2, \frac{44}{3}), Minimum (3, - 27)

Solution steps

f^{'} (x) = 2 x^{2} - 2 x - 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

\frac{2 x ^{3}}{3} - x^{2} - 12 x : \frac{44}{3}

Maximum (- 2, \frac{44}{3})

Plug

x = 3

into

\frac{2 x ^{3}}{3} - x^{2} - 12 x : - 27

Minimum (3, - 27)

Maximum (- 2, \frac{44}{3}), Minimum (3, - 27)

f (x) = x^{4} + 6 x^{3} + 24 x^{2} + 8 x + 1

f (x) = 3 x^{2} - 3 y^{2}

f (x, y) = x^{4} - 8 x^{3} + 22 x^{2} - 24 x

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

f (x, y) = x^{2} + y^{3} - 300 x - 75 y - 3

What is the extreme f(x)=(2x^3)/3-x^2-12x ?
The extreme f(x)=(2x^3)/3-x^2-12x is Maximum(-2, 44/3),Minimum(3,-27)