What is the extreme f(x)=-2/3 x^3-11/2 x^2-5x+1 ?

The extreme f(x)=-2/3 x^3-11/2 x^2-5x+1 is Minimum(-5,-169/6),Maximum(-1/2 , 53/24)

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extreme f(x)=-2/3 x^3-11/2 x^2-5x+1

extreme points

f (x) = - \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 1

Minimum (- 5, - \frac{169}{6}), Maximum (- \frac{1}{2}, \frac{53}{24})

Solution steps

f^{'} (x) = - 2 x^{2} - 11 x - 5

Find intervals:

Decreasing

: - \infty < x < - 5,

Increasing

: - 5 < x < - \frac{1}{2},

Decreasing

: - \frac{1}{2} < x < \infty

Plug

x = - 5

into

- \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 1 : - \frac{169}{6}

Minimum (- 5, - \frac{169}{6})

Plug

x = - \frac{1}{2}

into

- \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 1 : \frac{53}{24}

Maximum (- \frac{1}{2}, \frac{53}{24})

Minimum (- 5, - \frac{169}{6}), Maximum (- \frac{1}{2}, \frac{53}{24})

f (x, y) = x^{3} + y^{3} - 3 x - 12 y + 13 e

f (x) = - \frac{2}{3} x^{3} - \frac{11}{2} x^{2} - 5 x + 9

f (x) = x^{3} - 9 x^{2} + 27 x - 26

f (x) = \frac{x ^{2} - 10 x + 25}{x - 8}

f (x) = \frac{- 2}{3} x^{3} + 10 x^{2} - 48 x - 1

What is the extreme f(x)=-2/3 x^3-11/2 x^2-5x+1 ?
The extreme f(x)=-2/3 x^3-11/2 x^2-5x+1 is Minimum(-5,-169/6),Maximum(-1/2 , 53/24)