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. \(f ( 6 ) = 12\)

---

Definitions:

Corrective Action

Steps taken to rectify a problem or issue.

Deviations From Standards

Deviations from standards refer to instances where performance or output fails to meet established benchmarks or expectations.

Transactional Leaders

Leaders who focus on the exchange process between themselves and their followers, emphasizing task completion and performance rewards.

Genuine Desire

A sincere and authentic longing or aspiration without any ulterior motives or pretenses.