What is the extreme f(x)=-(40x)/(x^2+25) ?

The extreme f(x)=-(40x)/(x^2+25) is Maximum(-5,4),Minimum(5,-4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

extreme f(x)=-(40x)/(x^2+25)

extreme points

f (x) = - \frac{40 x}{x ^{2} + 25}

Maximum (- 5, 4), Minimum (5, - 4)

Solution steps

f^{'} (x) = - \frac{40 ( - x ^{2} + 25 )}{( x ^{2} + 25 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - 5,

Decreasing

: - 5 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = - 5

into

- \frac{40 x}{x ^{2} + 25} : 4

Maximum (- 5, 4)

Plug

x = 5

into

- \frac{40 x}{x ^{2} + 25} : - 4

Minimum (5, - 4)

Maximum (- 5, 4), Minimum (5, - 4)

cr i t i c a l x + \frac{4}{x}

a sy m pt o t es f (x) = \frac{( x - 1 )}{x + 1}

a sy m pt o t es f (x) = \frac{2 x ^{2} + 4 x}{x ^{2} - 2 x - 8}

sy mm e t ry y = x^{3} + 2 x - 1

d o main f (x) = 2 x - 8

What is the extreme f(x)=-(40x)/(x^2+25) ?
The extreme f(x)=-(40x)/(x^2+25) is Maximum(-5,4),Minimum(5,-4)