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

The extreme f(x)= 1/3 x^3-1/2 x^2-2x is Maximum(-1, 7/6),Minimum(2,-10/3)

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

extreme points

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

Maximum (- 1, \frac{7}{6}), Minimum (2, - \frac{10}{3})

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x : \frac{7}{6}

Maximum (- 1, \frac{7}{6})

Plug

x = 2

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x : - \frac{10}{3}

Minimum (2, - \frac{10}{3})

Maximum (- 1, \frac{7}{6}), Minimum (2, - \frac{10}{3})

f (x) = x^{3} - 3 x + 1, 0 \leq x \leq 5

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

f (x) = \frac{3 x}{2 x ^{2} + 2}, - 4 \leq x \leq 4

f (x) = cos (7 x)

What is the extreme f(x)= 1/3 x^3-1/2 x^2-2x ?
The extreme f(x)= 1/3 x^3-1/2 x^2-2x is Maximum(-1, 7/6),Minimum(2,-10/3)