AP Calculus AB and BC glossary
First derivative test
The first derivative test classifies a critical point by examining the sign of the derivative on both sides. A change from positive to negative gives a local maximum, negative to positive gives a local minimum, and no sign change means neither.
The practical method is a sign chart: mark every critical point and every point where is undefined on a number line, test one value in each resulting interval, and record the sign of there.
Unlike the second derivative test, this one never fails to give an answer, and it works at points where the derivative does not exist. That reliability is why it is the safer default.
Justify with the sign change
On free response, the credited justification names the sign change of , not the value of . Writing that changes from positive to negative at is what earns the point.
Appears in: Unit 5: Analytical Applications