AP Calculus AB and BC glossary
Constraint equation
A constraint equation is the extra relationship in an optimization problem that ties the variables together. You solve it for one variable and substitute into the objective function, which turns a two-variable problem into one you can differentiate.
It is usually the sentence with a fixed number in it: a fixed perimeter, a fixed volume, a fixed length of fence. The quantity being maximised or minimised is the objective, and the fixed one is the constraint.
The mistake
Differentiating the objective while it still has two variables. Substitute the constraint first, or the derivative you take is meaningless.
Appears in: Unit 5: Analytical Applications