Instructions: Answer Any Four (4) Questions. The questions cover Rolle's Theorem, Mean Value Theorem, relative extrema, absolute maximum/minimum, Lagrange Multiplier, directional derivative, and Taylor/Maclaurin Series.

Step 1: State Rolle's Theorem.
Rolle's Theorem states that if a function $f(x)$ is continuous on a closed interval $[a,b]$ and differentiable on the open interval $(a,b)$, and if $f(a) = f(b)$, then there exists at least one number $c$ in $(a,b)$ such that $f'(c) = 0$.

The statement of Rolle's Theorem is:
If $f$ is continuous on $[a,b]$, differentiable on $(a,b)$, and $f(a) = f(b)$, then there exists a number $c \in (a,b)$ such that $f'(c) = 0$.