What is the extreme f(x)=x-(-2)x^{-1} ?

The extreme f(x)=x-(-2)x^{-1} is Maximum(-sqrt(2),-2sqrt(2)),Minimum(sqrt(2),2sqrt(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

extreme

Maximum (- 2, - 22), Minimum (2, 22)

Solution steps

f^{'} (x) = 1 - \frac{2}{x ^{2}}

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 2

into

x - (- 2) x^{- 1} : - 22

Maximum (- 2, - 22)

Plug

x = 2

into

x - (- 2) x^{- 1} : 22

Minimum (2, 22)

Maximum (- 2, - 22), Minimum (2, 22)

What is the extreme f(x)=x-(-2)x^{-1} ?
The extreme f(x)=x-(-2)x^{-1} is Maximum(-sqrt(2),-2sqrt(2)),Minimum(sqrt(2),2sqrt(2))