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Popular >

extreme f(x)=-9+8x-x^3

Solution

extreme points

f (x) = - 9 + 8 x - x^{3}

Solution

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 9), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 9)

Solution steps

f^{'} (x) = - 3 x^{2} + 8

Find intervals:

Decreasing

: - \infty < x < - \frac{2 2}{3},

Increasing

: - \frac{2 2}{3} < x < \frac{2 2}{3},

Decreasing

: \frac{2 2}{3} < x < \infty

Plug

x = - \frac{2 2}{3}

into

- 9 + 8 x - x^{3} : - \frac{32 2}{3 3} - 9

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 9)

Plug

x = \frac{2 2}{3}

into

- 9 + 8 x - x^{3} : \frac{32 2}{3 3} - 9

Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 9)

Minimum (- \frac{2 2}{3}, - \frac{32 2}{3 3} - 9), Maximum (\frac{2 2}{3}, \frac{32 2}{3 3} - 9)

Popular Examples

domain of 2x^2-7x domain

2 x^{2} - 7 x

range of x^3-3 range

x^{3} - 3

range of 1/(x+7)range

\frac{1}{x + 7}

asymptotes of f(x)= 3/(x-3)asymptotes

f (x) = \frac{3}{x - 3}

line (-2,0),(2,0)line

(- 2, 0), (2, 0)

Frequently Asked Questions (FAQ)

What is the extreme f(x)=-9+8x-x^3 ?
The extreme f(x)=-9+8x-x^3 is