Given $f(x)=2 x^{3}-$ $3 x^{2}-36 x+6$ (A) Find the Intervals on Which F Is Increasing

Given $f(x) =2 x^{3}-$$3 x^{2}-36 x+6$ . (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 $(-\infty,-2)$ and $(3, \infty)$ decreasing on $(-2,3)$
(b) Rel. max. $f(-2) =50$ ,
Rel) min. $f(3) =-75$
B) (a) Increasing on $(-\infty,-3)$ and $(2, \infty)$ decreasing on $(-3,2)$
(b) Rel. max. $f(-3) =33$ ,
Rel) min. $f(2) =-62$
C) (a) Increasing on $(-3,2)$ , decreasing on $(-\infty,-3)$ and $(2, \infty)$
(b) Rel. max. $f(2) =62$ ,
Rel) min. $f(-3) =-33$
D) (a) Increasing on $(-2,3)$ , decreasing on $(-\infty,-2)$ and $(3, \infty)$
(b) Rel. max. $f(3) =75$ ,
Rel) min. $f(-2) =-50$

Correct Answer:

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