Applications of differentiation: (1) Rate of change: f'(x) = instantaneous rate; (2) Velocity: v = ds/dt, acceleration a = dv/dt; (3) Optimization: Find maxima/minima for max profit, min cost; (4) Elasticity: E = (dQ/dP) × (P/Q); (5) Marginal analysis: Marginal cost = dC/dQ, marginal revenue = dR/dQ. Example: Cost C(x) = 100 + 5x + 0.5x². Marginal cost = dC/dx = 5 + x. At x=10, MC = 15. Revenue R(x) = 20x. Marginal revenue = 20 (constant). Profit P(x) = R - C = 20x - 100 - 5x - 0.5x² = 15x - 100 - 0.5x². dP/dx = 15 - x. Max profit when dP/dx = 0 → x = 15. Exam tip: Interpret derivatives in business context. Practice: Word problems with rates and optimization.