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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Definitions:

Materials Quantity Variance

A calculation that shows the difference between the actual amount of materials used and the expected amount, which can indicate issues in efficiency or procurement.

Materials Price Variance

The difference between the actual cost of materials and the standard or expected cost, used to assess cost management efficiency.

Materials Quantity Variance

Materials Quantity Variance is the difference between the expected amount of materials to produce a given output and the actual amount of materials used, highlighting efficiency in material usage.

Variable Overhead

Expenses that vary with production volume, such as utility costs in a factory.