What is the extreme f(x)= 1/3 x^3-1/2 x^2-6x ?

The extreme f(x)= 1/3 x^3-1/2 x^2-6x is Maximum(-2, 22/3),Minimum(3,-27/2)

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extreme f(x)= 1/3 x^3-1/2 x^2-6x

extreme points

f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - 2

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : \frac{22}{3}

Maximum (- 2, \frac{22}{3})

Plug

x = 3

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 6 x : - \frac{27}{2}

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

Maximum (- 2, \frac{22}{3}), Minimum (3, - \frac{27}{2})

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

\frac{x ^{2} + x - 38}{x ^{2} - 25}

f (x) = x^{\frac{4}{5}} (9 - 4 x)

f (x) = - \frac{1}{2} x^{4} + 8 x^{3} - 32 x^{2} - 5

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

What is the extreme f(x)= 1/3 x^3-1/2 x^2-6x ?
The extreme f(x)= 1/3 x^3-1/2 x^2-6x is Maximum(-2, 22/3),Minimum(3,-27/2)