Science:Math Exam Resources/Courses/MATH104/December 2013/Question 02 (e)/Solution 1

From parts (b), we can see that there's no inflection point. On the other hand, using parts (a) and parts (c) we can see that the extrema can only occur possible at $\displaystyle x=0$, $x=\pm 2$. Since the latter two points are not in the domain, we need only to check the point $\displaystyle x=0$ for extrema. Looking at parts (c), we see to the immediate left of 0, the function is increasing and to its immediate right the function is decreasing. Thus this point is a local maximum. The coordinates are given by $\displaystyle (0,0)$ found by plugging in 0 into the original function.