- Fromthe exampleabove,we foundthatf(x) = 2x, so
This meansthat the instantaneousrate of changeis negative.That is,yis decreasingat It is de-
creasingat a rate of 1 unit per unit increaseinx.
ReviewQuestions
- Giventhe functiony= 1/2 x^2 and the valuesofx 0 = 3 andx 1 = 4, find
a. The averagerate of changeofywith respecttoxover the interval[x 0 ,x 1 ].
b. The instantaneousrate of changeofywith respecttoxatx 0.
c. The slopeof the tangentline atx 1.
d. The slopeof the secantline betweenpointsx 0 andx 1.
e. Makea sketchofy= 1/2x^2 and showthe secantand tangentlines at their respectivepoints.- Repeatproblem#1 forf(x) = 1/x and the valuesx 0 = 2 andx 1 = 3.
- Find the slopeof the graphf(x) =x^2 + 1 at a generalpointx. Whatis the slopeof the tangentline atx 0
= 6? - Supposethat.
a. Find the averagerate of changeofywith respecttoxover the interval[1,3].
b. Find the instantaneousrate of changeofywith respecttoxat pointx= 1. - A rocketis propelledupwardand reachesa heightofh(t) = 4.9t^2 intseconds.
a. How high doesit reachin 35 seconds?
b. Whatis the averagevelocityof the rocketduringthe first 35 seconds?
c. Whatis the averagevelocityof the rocketduringthe first 200 meters?
d. Whatis the instantaneousvelocityof the rocketat the end of the 35 seconds? - A particlemovesin the positivedirectionalonga straightline so that aftertnanoseconds,its traversed
distanceis givenby nanometers.
a. Whatis the averagevelocityof the particleduringthe first 2 nanoseconds?