Given $f ( x ) = x ^ { 2 } + 6 x$

Given $f ( x ) = x ^ { 2 } + 6 x$ .
(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 $( - 3 , \infty )$ ,
decreasing on $( - \infty , - 3 )$
(b) Rel. min. $f ( - 3 ) = - 9$
B) (a) Increasing on $( - \infty , - 3 )$ ,
decreasing on $( - 3 , \infty )$
(b) Rel. max. $f ( - 3 ) = - 9$
C) (a) Increasing on $( - 6 , \infty )$ ,
decreasing on $( - \infty , - 6 )$
(b) Rel. min. $f ( - 6 ) = 0$
D) (a) Increasing on $( - \infty , - 6 )$ ,
decreasing on $( - 6 , \infty )$
(b) Rel. max. $f ( - 6 ) = 0$

Correct Answer:

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