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^5-3x^3-3x+1

Solution

extreme points

f (x) = 4 x^{5} - 3 x^{3} - 3 x + 1

Solution

Maximum (- \frac{9 + 321}{2 10}, \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1), Minimum (\frac{9 + 321}{2 10}, - \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1)

Solution steps

f^{'} (x) = 20 x^{4} - 9 x^{2} - 3

Find intervals:

Increasing

: - \infty < x < - \frac{9 + 321}{2 10},

Decreasing

: - \frac{9 + 321}{2 10} < x < \frac{9 + 321}{2 10},

Increasing

: \frac{9 + 321}{2 10} < x < \infty

Plug

x = - \frac{9 + 321}{2 10}

into

4 x^{5} - 3 x^{3} - 3 x + 1 : \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1

Maximum (- \frac{9 + 321}{2 10}, \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1)

Plug

x = \frac{9 + 321}{2 10}

into

4 x^{5} - 3 x^{3} - 3 x + 1 : - \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1

Minimum (\frac{9 + 321}{2 10}, - \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1)

Maximum (- \frac{9 + 321}{2 10}, \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1), Minimum (\frac{9 + 321}{2 10}, - \frac{3 ( 89 + 321 ) 9 + 321}{200 10} + 1)

Graph

Popular Examples

extreme f(x,y)=2xy-5x^2-2y^2+4x+4y-4 extreme points

f (x, y) = 2 x y - 5 x^{2} - 2 y^{2} + 4 x + 4 y - 4

extreme w(x,y)=6+(3xy)/(75)extreme points

w (x, y) = 6 + \frac{3 x y}{75}

extreme f(x)=14xy-x^3-7y^2 extreme points

f (x) = 14 x y - x^{3} - 7 y^{2}

extreme x^{4/3}(7x^2+10x-210)extreme points

x^{\frac{4}{3}} (7 x^{2} + 10 x - 210)

extreme f(x)=-x^3+3x^2-8 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)=4x^5-3x^3-3x+1 ?
The extreme f(x)=4x^5-3x^3-3x+1 is