- Thereare no maximumsor minimums;no relativemaximumsor minimums.
The SecondDerivativeTest
LearningObjectives
A studentwill be able to:
- Find intervalswherea functionis concaveupwardor downward.
- Applythe SecondDerivativeTest to determineconcavityand sketchgraphs.
Introduction
In this lessonwe will discussa propertyaboutthe shapesof graphscalledconcavity, and introducea method
with whichto studythis phenomenon,the SecondDerivativeTest. This methodwill enableus to identify
preciselythe intervalswherea functionis eitherincreasingor decreasing,and also help us to sketchthe
graph.
Definition A function is said to be concaveupward on containedin the domainof if is
an increasingfunctionon andconcavedownwardon if is a decreasingfunctionon
Hereis an examplethat illustratestheseproperties.