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

The extreme f(x)= 1/3 x^3-1/2 x^2-2x+1 is Maximum(-1, 13/6),Minimum(2,-7/3)

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

extreme points

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

Maximum (- 1, \frac{13}{6}), Minimum (2, - \frac{7}{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 + 1 : \frac{13}{6}

Maximum (- 1, \frac{13}{6})

Plug

x = 2

into

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

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

Maximum (- 1, \frac{13}{6}), Minimum (2, - \frac{7}{3})

f (x) = (x + 1)^{7} - 7 x - 3

f (x) = - x^{2} + 4 x y - 5 y^{2} - 6 x + 22 y + 9

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

f (x, y) = x^{4}

f (x) = (x - 5) (x + 2)

What is the extreme f(x)= 1/3 x^3-1/2 x^2-2x+1 ?
The extreme f(x)= 1/3 x^3-1/2 x^2-2x+1 is Maximum(-1, 13/6),Minimum(2,-7/3)