Science:Math Exam Resources/Courses/MATH104/December 2015/Question 02 (b)/Hint 1

Recall Fermat's theorem (which you may have encountered under a different name). It states that if $f$ is a differentiable function on some open interval $(a,b)$ and $c\in (a,b)$ is a local extremum of $f,$ then $f'(c)=0.$ In the context of this problem, this means that points in $(-1,1)$ where $f'$ is zero are possible locations of local maxima.