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

The extreme f(x)= 1/3 x^3+1/2 x^2-2x+2 is Maximum(-2, 16/3),Minimum(1, 5/6)

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

extreme points

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

Maximum (- 2, \frac{16}{3}), Minimum (1, \frac{5}{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 + 2 : \frac{16}{3}

Maximum (- 2, \frac{16}{3})

Plug

x = 1

into

\frac{1}{3} x^{3} + \frac{1}{2} x^{2} - 2 x + 2 : \frac{5}{6}

Minimum (1, \frac{5}{6})

Maximum (- 2, \frac{16}{3}), Minimum (1, \frac{5}{6})

f (x) = 4 x^{5} + 25 x^{4} - 40 x^{3} - 1

f (x, y) = 6 x y

f (x) = x x^{2} + 25, - 6 \leq x \leq 4

(- 2.3) (1)

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

What is the extreme f(x)= 1/3 x^3+1/2 x^2-2x+2 ?
The extreme f(x)= 1/3 x^3+1/2 x^2-2x+2 is Maximum(-2, 16/3),Minimum(1, 5/6)