SL 5.7—Optimization
- Syllabus
- First assessment 2021
- Objective
- —
- Level
- SL
Optimization chooses the best feasible value, not merely a stationary one
Optimization maximises or minimises a specified objective subject to constraints. Calculus can locate interior candidates where the derivative is zero, but endpoints, feasibility and the meaning of the variables decide the answer.
Translate the context into an objective function, state the domain, solve for critical points and compare all feasible candidates. A minimum cost or maximum area is a claim about the whole allowed interval, not just a local curve shape.
For a rectangle with fixed perimeter 20, A=x(10−x) on 0<x<10. A'(x)=10−2x gives x=5, and comparing the endpoints' limiting values confirms the square gives the largest area.
A stationary point is not automatically the global optimum. Check the full feasible domain and endpoints, state units, and interpret the best value in context. Kinematics questions are not set in SL examinations.