Finding the Best Decision

Business Calculus · Axiom Academy

INTRO Finding the Best Decision Using calculus to optimize business outcomes The Ultimate Business Question Every business faces the same fundamental challenge: How do we make the best possible decisions? Maximum profit? Minimum cost? Optimal price? Calculus gives us the tools to find these answers precisely. Think about the decisions businesses make every day: How many units should we produce to maximize profit? What price maximizes our total revenue? What production level minimizes average cost? How do we allocate our budget for maximum return? When we graph profit, revenue, or cost functions, optimal points appear as peaks (maxima) or valleys (minima). At the top of a hill (maximum) or bottom of a valley (minimum), the curve is momentarily flat . The tangent line is horizontal, which means the derivative equals zero! This is the foundation of optimization: optimal points occur where the rate of change is zero . Our optimization strategy follows a clear mathematical process: Critical Points: Where the Action Happens Points where f'(x) = 0 (or is undefined) are called critical points . These are our candidates for optimal values. If f(x) has a maximum or minimum at x = c (and f is differentiable there), then f'(c) = 0 Function increases then decreases. Derivative goes from positive to negative. Function decreases then increases. Derivative goes from negative to positive.

This is the written version of the interactive lesson above. See the full Business Calculus course.