The Mean Value Theorem (MVT) says that if a function is continuous on [a,b] and differentiable on (a,b), there must be at least one point c inside the interval where the instantaneous rate of change equals the average rate of change. This guide covers the formal statement, geometric intuition with parallel tangent and secant lines, Rolle's theorem as the special case, how to check the continuity and differentiability hypotheses, a step-by-step procedure for finding c, common mistakes on AP free-response problems, and applications to physics, monotonicity, and inequality proofs.