Chapter 6 · Test 1
One-Variable Optimization
First- and second-order conditions and optimization on intervals.
What you will learn
- Find an unconstrained maximum
- Optimize on a closed interval
- Use the second-order condition
Reasoning habits that help
- A zero first derivative locates a candidate; negative curvature verifies a local maximum.
- On a closed interval, endpoints are candidates even when they do not satisfy the interior first-order condition.
- The first derivative finds candidates; the second derivative classifies them through curvature.
Where economists use these methods
- Firms use one-variable optimization to choose output, price, advertising, or another decision that maximizes profit.
- Bounded optimization models choices constrained by capacity, budgets, regulations, or nonnegativity.
- Second-order conditions distinguish profit or utility maxima from cost minima and unstable stationary points.