3. Applicationsof Derivatives.........................................................................................................
RelatedRates
LearningObjectives
A studentwill be able to:
- Solveproblemsthat involverelatedrates.
Introduction
In this lessonwe will discusshow to solveproblemsthat involverelatedrates.Relatedrate problemsinvolve
equationswherethereis somerelationshipbetweentwo or morederivatives.We solvedexamplesof such
equationswhenwe studiedimplicitdifferentiationin Lesson2.6. In this lessonwe will discusssomereal-life
applicationsof theseequationsand illustratethe strategiesone usesfor solvingsuchproblems.
Let’s start our discussionwith somefamiliargeometricrelationships.
Example1:PythagoreanTheorem
We couldeasilyattachsomereal-lifesituationto this geometricfigure.Say for instancethat and rep-
resentthe pathsof two peoplestartingat point and walkingNorthand West, respectively, for two hours.
The quantity representsthe distancebetweenthemat any time Let’s now see somerelationshipsbe-
tweenthe variousratesof changethat we get by implicitlydifferentiatingthe originalequation
with respectto time