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

question 169

Multiple Choice

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. \(f(-1)=-2\)

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