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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