What is the extreme f(x)= 1/3 x^3-3/2 x^2-18x+1/3 ?

The extreme f(x)= 1/3 x^3-3/2 x^2-18x+1/3 is Maximum(-3, 191/6),Minimum(6,-269/3)

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extreme f(x)= 1/3 x^3-3/2 x^2-18x+1/3

extreme points

f (x) = \frac{1}{3} x^{3} - \frac{3}{2} x^{2} - 18 x + \frac{1}{3}

Maximum (- 3, \frac{191}{6}), Minimum (6, - \frac{269}{3})

Solution steps

f^{'} (x) = x^{2} - 3 x - 18

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 6,

Increasing

: 6 < x < \infty

Plug

x = - 3

into

\frac{1}{3} x^{3} - \frac{3}{2} x^{2} - 18 x + \frac{1}{3} : \frac{191}{6}

Maximum (- 3, \frac{191}{6})

Plug

x = 6

into

\frac{1}{3} x^{3} - \frac{3}{2} x^{2} - 18 x + \frac{1}{3} : - \frac{269}{3}

Minimum (6, - \frac{269}{3})

Maximum (- 3, \frac{191}{6}), Minimum (6, - \frac{269}{3})

\frac{2 x - 6}{x + 3}

f (x, y) = x y + x^{2} + y^{2} + x - y + 17

f (x) = 4 x - 7 x^{\frac{4}{7}}

f (x) = 25 x - 25 x e^{- y} - 50 y - x^{2}

f (x, y) = x^{2} + x y - 10 x + y^{2} - 11 y + 37

What is the extreme f(x)= 1/3 x^3-3/2 x^2-18x+1/3 ?
The extreme f(x)= 1/3 x^3-3/2 x^2-18x+1/3 is Maximum(-3, 191/6),Minimum(6,-269/3)