en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

extreme f(x)=4x-2x^3-5

Solution

extreme points

f (x) = 4 x - 2 x^{3} - 5

Solution

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5), Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Solution steps

f^{'} (x) = - 6 x^{2} + 4

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{2}{3}

into

4 x - 2 x^{3} - 5 : - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Plug

x = \frac{2}{3}

into

4 x - 2 x^{3} - 5 : 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5

Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5), Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Popular Examples

range of sqrt(x^2-10)range

x^{2} - 10

domain of f(x)=-ax domain

f (x) = - a x

domain of f(x)= 1/x+1/(x-3)+1/(x-2)domain

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

extreme y=x^3-2x^2-4x+3 extreme points

y = x^{3} - 2 x^{2} - 4 x + 3

domain of f(x)=4x-12 domain

f (x) = 4 x - 12

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x-2x^3-5 ?
The extreme f(x)=4x-2x^3-5 is