AP Calculus AB and BC glossary
Candidates test
Also called: Closed interval method
The candidates test finds absolute extrema on a closed interval by evaluating the function at every critical point and at both endpoints, then comparing the resulting values. The largest is the absolute maximum and the smallest is the absolute minimum.
It works because the Extreme Value Theorem guarantees the extrema exist and restricts where they can be. With only finitely many candidates, comparing function values settles the question completely.
The mistake
Comparing derivative values instead of function values. The candidates are located using , but the comparison that decides the answer uses .
Appears in: Unit 5: Analytical Applications