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

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

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

extreme points

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

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 3

into

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

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

Plug

x = 2

into

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

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

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

f (x, y) = 5 x y - 7 x^{2} + 3 x - 6 y + 2

f (x) = \frac{x ^{2} - 16}{x ^{2} + 16}

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

f (x) = - x^{4} + 4 x^{3} + 8 x^{2}

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

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