en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

extreme points

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

Solution

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} - 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} - 1)

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{2}{3}

into

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

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} - 1)

Plug

x = \frac{2}{3}

into

x^{3} - 2 x - 1 : (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} - 1

Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} - 1)

Maximum (- \frac{2}{3}, - (\frac{2}{3})^{\frac{3}{2}} + 2 \frac{2}{3} - 1), Minimum (\frac{2}{3}, (\frac{2}{3})^{\frac{3}{2}} - 2 \frac{2}{3} - 1)

Popular Examples

y = x^{2} + 4 x + 4

domain of cos(3t)domain

cos (3 t)

critical f(x)=3-3x+3x^2-x^3 critical points

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

perpendicular y=-1/4 x+3,(3,-3)perpendicular

y = - \frac{1}{4} x + 3, (3, - 3)

domain of f(x)=-(31)/((6+t)^2)domain

f (x) = - \frac{31}{( 6 + t ) ^{2}}

Frequently Asked Questions (FAQ)

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