What is the extreme 1/3 x^3-1/2 x^2-2x ?

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

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extreme 1/3 x^3-1/2 x^2-2x

extreme points

\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, y) = x^{3} - y^{3} - 3 x y

f (x) = x^{2} + y^{2} + 1

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

f (x) = - 5 x^{2} + 50 x - 80

f (x) = 1 - 7 x^{2}

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