Question 1
If $f$ is differentiable on an open interval and has a local maximum at an interior point $c$, what must be true about $f'(c)$?
Question 2
Which conditions are required to use the Mean Value Theorem on $[a,b]$?
Question 3
Suppose $f$ is continuous on $[a,b]$, differentiable on $(a,b)$, and $f(a)=f(b)$. What does Rolle's Theorem guarantee?
Question 4
If $f'(x)>0$ for every $x$ in an interval, what can be concluded about $f$ on that interval?
Question 5
If $f'(x)<0$ for every $x$ in an interval, what can be concluded about $f$ on that interval?
