Name the objective
Area, volume, cost, revenue, profit or distance must be written explicitly before calculus begins.
IB MATHEMATICS AA HL · TOPIC 5 · CALCULUS
Optimization
Optimization taught as modelling first and differentiation second. The notes move through geometric shapes, surface area and volume, distance, material cost, revenue and profit, with diagrams, hints, decision steps and difficult multi-part IB-style questions.
THE OPTIMIZATION STORY
Translate the situation before differentiating anything.
Each example follows the same disciplined route: identify the quantity to maximize or minimize, write the constraint, reduce the model to one variable, establish a meaningful domain, differentiate, locate candidates and justify the final optimum. Diagrams and hints make the modelling decisions visible rather than hiding them inside algebra.
Reduce to one variable
Use perimeter, surface area, volume or demand information to eliminate extra variables.
Find and classify candidates
Use derivative sign or second-derivative evidence, and remember endpoints when the domain is closed.
Return to the original question
Give the requested dimensions, units and economic or geometric meaning rather than stopping at an x-value.
TOPIC 5 BUNDLE
Included in Topic 5 · Calculus · €50
The revised Optimization lecture notes are included with the full current Calculus library.
Open the complete Topic 5 bundle →