Given $f(x)=x+\frac{1}{x}$ (A) Find the Intervals on Which F Is Increasing

Given $f(x) =x+\frac{1}{x}$ . (a) Find the intervals on which f is increasing or decreasing.
(b) Find the relative maxima and relative minima of f.

A) (a) Increasing on $(-1,0)$ and $(0,1)$ decreasing on $(-\infty,-1)$ and $(1, \infty)$
(b) Rel. max. $f(1) =2$ ,
Rel) min. $f(-1) =-2$
B) (a) Increasing on $(-\infty,-1)$ and $(1, \infty)$ , decreasing on $(-1,0)$ and $(0,1)$
(b) Rel. max. $f(-1) =-2$ ,
Rel) min. $f(1) =2$
C) (a) Increasing on $(-\infty,-1)$ and $(1, \infty)$ , decreasing on $(-1,1)$
(b) Rel. max. $f(-1) =-2$ ,
Rel) min. $f(1) =2$
D) (a) Increasing on $(-1,1)$ , decreasing on $(-\infty,-1)$ and $(1, \infty)$
(b) Rel. max. $f(1) =2$ ,
Rel) min. $f(-1) =-2$

Correct Answer:

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