# Average and Instantaneous Rate of Change and Application to Revenue

Find the average rate of change of the function over the indicated interval. Than compare the average rate of change to the instantaneous rate of change at the end points of the interval.

f(x)= x^2 + 3x - 4; (0,1)

The annual revenue R (in millions of $ per year) of Wm. Wrigley Jr. Company for the years 1994-2000 can be modeled by

R= 2.0472t^3 - 49.642t^2 + 466.48t + 396.7

when t=4 corresponds to 1994.

a.) Find the average rate of change for the interval from 1996 to 2000

b.) Find the instantaneous rate of change of the model for 1996 and 2000

c.) Interpret the results of part a.) and b.) in the context of the problem

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#### Solution Preview

part 1

f'(x) = 2x + 3

f'(0) = 3

f'(1) = 5

average rate of change from 0 to 1 = [f(1) - f(0)] / (1-0) = [0 - (-4)] / (1 -0) = 4

The average rate of change is the average of 3 and ...

#### Solution Summary

Average and instantaneous rate of change are investigated. This is applied to revenue calculations.