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

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. $f ( 6 ) = 12$

Correct Answer:

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