Given $f ( x ) = x + \frac { 36 } { x }$

question 68

Multiple Choice

Given $f ( x ) = x + \frac { 36 } { x }$ .
(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 \(( - 6,6 )\), decreasing on \(( - \infty , - 6 )\) and \(( 6 , \infty )\)
• (b) Rel. \(\max . f ( 6 ) = 12\),
• rel. min. \(f ( - 6 ) = - 12\)
• B) (a) Increasing on \(( - 6,0 )\) and \(( 0,6 )\), decreasing on \(( - \infty , - 6 )\) and \(( 6 , \infty )\)
• (b) Rel. \(\max . f ( 6 ) = 12\),
• rel. min. \(f ( - 6 ) = - 12\)
• C) (a) Increasing on \(( - \infty , - 6 )\) and \(( 6 , \infty )\), decreasing on \(( - 6,0 )\) and \(( 0,6 )\)
• (b) Rel. max. \(f ( - 6 ) = - 12\),
• rel. min. \(f ( 6 ) = 12\)
• D) (a) Increasing on \(( - \infty , - 6 )\) and \(( 6 , \infty )\), decreasing on \(( - 6,6 )\)
• (b) Rel. max. \(f ( - 6 ) = - 12\),
• rel. min. \(f ( 6 ) = 12\)

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Definitions:

Short Run

A period in economics during which some factors of production are fixed, limiting the ability of a business to expand or change its output levels.

Industry

A group of companies that produce similar goods or services, engaged in the same type of business.

Variable Costs

Variable costs are expenses that vary directly with the level of production or output, such as materials and labor used in the manufacturing process.

Fixed Costs

Expenses that do not change with the level of output or sales, such as rent, salaries, and insurance premiums.