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(-2, 10/3),Minimum(1,-7/6)

Popular >

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

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

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

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

Plug

x = 1

into

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

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

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

f (x) = 12 x - x^{3} - y (y^{2} + 3 y - 9) + 4

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

f (x) = 64 - x^{2}

f (x, y) = x y - 4 y - 16 x + 64

y = cos (x)

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(-2, 10/3),Minimum(1,-7/6)