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 (a,b) such that f'(c) = 0. Send me the next one 📸