   Chapter 10.5, Problem 120E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Give a numerical explanation of the fact that if f is a linear function, then the average rate of change over any interval equals the instantaneous rate of change at any point.

To determine

The average rate of change in any interval is equal to the instantaneous rate of change at any point for a linear function with the help of numerical method.

Explanation

Consider a linear function which is in the form y=mx+c where m is the slope and c is the y-intercept

The difference quotient method over the interval [a,a+h] is f(a)f(a+h)f(a)h

Consider a point p,

Evaluate the average rate of change over intervals [p,p+h], by substituing h=1,0.1,0.001 and 0.00001

For h=1,

f(p)f(p+h)f(p)hf(p)(m(p+h)+c)(mp+c)hf(p)mp+mh+cmpchf(p)m

For h=0

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