AverageandInstantaneousVelocity

Youdriveacarfor2hoursandtravel90km. Whatisyouraveragevelocity? distance rate= time 90 = 2 =45km/hr

100 B distance(km) 50 A 1 2 time(hrs)

100 B f(2)f(1)= distancetraveled distance(km) 50 A 21=timeelapsed 1 2 time(hrs)

AveragevelocitybetweenpointsAandpointB? distancetraveled AV= timeelapsed rise = run =slopeoflineAB

Ingeneral: Theaveragevelocityoveranyintervalistheslopeof thelinejoiningtheendpointsoftheinterval. Thislineiscalledasecantline.

B f(a+h)f(a) distance A h a a+h time f(a+h)f(a) averagevelocity= h

B B f(a+h)f(a) distance B A tangentline a a+h time

InstantaneousVelocity(att=a) lim f(a+h)f(a) = h0 h Thislimitingvalueistheslopeofthetangentlinetothe curveatpointAasthetimeintervalgetsshorter.

Findtheslopeofthetangentlineatx=1onf(x)=x2.

Exercise2.1 Questions111oddquestions

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