Calculus 1 — 12.4: Marginal Cost and Derivatives скачать в хорошем качестве

Calculus 1 — 12.4: Marginal Cost and Derivatives

Why does producing your 150th widget cost $20 less than your 100th? This video breaks down marginal cost—the derivative of the cost function—and shows how calculus quantifies the exact cost of producing one additional unit. You'll learn why costs don't increase uniformly, how fixed costs spread across production volume, and the mathematical basis for economies of scale. Key concepts covered: • The cost function C(x) and why it curves rather than rises linearly • Fixed costs (overhead) and the y-intercept of cost functions • Marginal cost as C'(x)—the derivative measuring instantaneous rate of cost change • Calculating marginal cost: C'(x) = -0.4x + 200 worked examples • The -0.4 coefficient: each unit costs 40 cents less than the previous • Economies of scale: bulk purchasing, labor efficiency, and fixed cost spreading • Marginal cost vs. average cost—different numbers, different purposes • U-shaped marginal cost curves and diseconomies of scale • Production decisions: comparing marginal cost to selling price ORIGINAL SOURCE This video distills concepts from:    • Calculus 1 Lecture 2.4:  Applications of t...   Full credit to the original creator for the educational content.