Science:Math Exam Resources/Courses/MATH110/April 2016/Question 05 (f)/Hint 1

Recall the first derivative test for local extremes;

Let $f$ be a continuous function with $f^{\prime }(a)=0$ or $f^{\prime }(a)$ is undefined.

(i) If $f^{\prime }$(left of $a$) $>0$ and $f^{\prime }$(right of $a$) $<0$, then $(a,f(a))$ is a local maximum

(i) If $f^{\prime }$(left of $a$) $<0$ and $f^{\prime }$(right of $a$) $>0$, then $(a,f(a))$ is a local minimum.