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

question 27

Multiple Choice

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. \(f(-2)=-50\)

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