What is the extreme f(x)= 1/3 x^3-1/2 x^2-2x+4/3 ?

The extreme f(x)= 1/3 x^3-1/2 x^2-2x+4/3 is Maximum(-1, 5/2),Minimum(2,-2)

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extreme f(x)= 1/3 x^3-1/2 x^2-2x+4/3

extreme points

f (x) = \frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x + \frac{4}{3}

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

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{4}{3} : \frac{5}{2}

Maximum (- 1, \frac{5}{2})

Plug

x = 2

into

\frac{1}{3} x^{3} - \frac{1}{2} x^{2} - 2 x + \frac{4}{3} : - 2

Minimum (2, - 2)

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

- 3 sin (2 x) - 4

f (x) = tan (x), - \frac{π}{6} \leq x \leq \frac{π}{4}

f (x) = x^{4} - 4 x^{3} - 8

x, f = x^{2} - 4 x y + y^{2}

f (x) = x^{\frac{2}{5}} (3 x + 7)

What is the extreme f(x)= 1/3 x^3-1/2 x^2-2x+4/3 ?
The extreme f(x)= 1/3 x^3-1/2 x^2-2x+4/3 is Maximum(-1, 5/2),Minimum(2,-2)