Science:Math Exam Resources/Courses/MATH110/April 2016/Question 09 (b)/Hint 1

Note that ${\frac {f(2)-f(-1)}{2-(-1)}}=2$, and try to imagine a function that does satisfy $f''<0$ everywhere and $f'(2)=3$. To determine whether such a function exists, sketch an example of a differentiable function that satisfies $f(-1)=-1$, $f(2)=2$, and $f'(2)=3$, then try to use the Mean Value Theorem (as many times as you need to) to explain why your drawings end up the way they do.