Simplifying,we have
Equation1.
So we haverelationshipsbetweenthe derivatives,and sincethe derivativesare rates,this is an example
ofrelatedrates. Let’s say that person is walkingat mph and that person is walkingat mph.The
rate at whichthe distancebetweenthe two walkersis changingat any time is dependenton the ratesat
whichthe two peopleare walking.Can you thinkof any problemsyou couldposebasedon this information?
One problemthat we couldposeis at whatrate is the distancebetween and increasingafter one hour.
That is, find
Solution:
Assumethat they havewalkedfor one hour. So mi and Usingthe PythagoreanTheorem,
we find the distancebetweenthemafter one hour is miles.
If we substitutethesevaluesintoEquation 1 alongwith the individualrateswe get
Henceafter one hour the distancebetweenthe two peopleis increasingat a rate of
.
Our secondexamplelists variousformulasthat are foundin geometry.
As with the PythagoreanTheorem,we knowof otherformulasthat relatevariousquantitiesassociatedwith
geometricshapes.Thesepresentopportunitiesto poseand solvesomeinterestingproblems
Example2:Perimeterand Areaof a Rectangle