Differential calculus and applications

Differentiation measures how fast a function changes: the derivative is the slope of the tangent, the marginal concept of economics. Marginal cost is the derivative of total cost, marginal utility the derivative of utility, and maximising a function means finding where its derivative is zero (and checking the second derivative is negative). Worked example: for total revenue TR = 100Q - 2Q^2, marginal revenue is MR = 100 - 4Q; setting MR = 0 gives Q = 25, the revenue-maximising output, and total revenue there is 100 x 25 - 2 x 625 = 1250.