Science:Math Exam Resources/Courses/MATH110/April 2016/Question 05 (f)/Hint 2

(For the alternative solution) Recall the second derivative test for extremes:

(1) If $f'(x)=0$ and ${\textstyle f''(x)<0}$, then ${\textstyle f}$ has a local maximum at ${\textstyle x}$;

(2) If $f'(x)=0$ and ${\textstyle f''(x>0)}$, then ${\textstyle f}$ has a local minimum at ${\textstyle x}$;