AP Calculus AB and BC glossary

Objective function

Also called: Constraint

The objective function in an optimization problem is the quantity being maximized or minimized. The constraint is a separate equation relating the variables, used to rewrite the objective in terms of a single variable before differentiating.

Telling them apart is the whole setup. The objective is whatever the question asks you to make largest or smallest; the constraint is the fixed condition, such as a given perimeter or a fixed volume.

The mistake

Differentiating the constraint instead of the objective. The constraint exists only to eliminate a variable; the derivative you set to zero belongs to the objective.

Appears in: Unit 5: Analytical Applications