Science:Math Exam Resources/Courses/MATH104/December 2012/Question 02 (c)/Solution 1

By part(a) and part(b) of this problem we see that the function changes from increasing to decreasing at $x=-3$, so there is a local maximum there, and the function changes from decreasing to increasing at $x=3$, so there is a local minimum at x=3. The function changes concavity at $x=0$, so there is an inflection point at x = 0.

(Notice that $x=\pm {\sqrt {3}}$ are not points in the domain and hence cannot be extrema or inflection points.)