   Chapter 10, Problem 31RE 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

In Exercises 31-34, find the average rate of change of the given function overt the interval [ a , a + h ] for h = 1 , 0.01 , and 0.001. (Round answers to four decimal places.) Then estimate the slope of the tangent line to the graph of the function at a. f ( x ) = 1 x + 1 ; a = 0

To determine

To calculate: The average rate of change for the function f(x)=1x+1 over the interval [a,a+h], when a=0 and h=1,0.01 and 0.001. Also estimate the slope of the tangent line to the function f(x) at a=0.

Explanation

Given information:

The provided function is f(x)=1x+1 and evaluate the average rate of change when a=0.

Formula used:

The formula for the average rate of change of function f(x) over the interval [a,a+h] is as follows:

Average rate of change of f(x)=f(a+h)f(a)h.

Calculation:

Consider the function, f(x)=1x+1 and calculate the average rate of change when a=0.

The average rate of change of function f(x) over the interval [a,a+h] is:

f(a+h)f(a)h.

Average rate of change of f(x) over [0,0+h] is f(0+h)f(0)h.

Now, calculate the average rate of change for different values of h which is follows:

For h=1,

Evaluate the values of f(0) and f(0+1) as:

f(0)=10+1=1

And,

f(0+1)=10+1+1=12=0.5

Substitute the values of f(0) and f(0+1) in the expression f(0+1)f(0)h to calculate the average rate of change of function C(x) as,

f(x)=f(0+1)f(0)h=0.511=0.5

For h=0.01,

Evaluate the values of f(0) and f(0+0.01) as:

f(0)=10+1=1

And,

f(0+0.01)=10+0.01+1=11.01=0.990099

Substitute the values of f(0) and f(0+0.01) in the expression f(0+0.01)f(0)h to calculate the average rate of change of function f(x) as,

f(x)=f(0+0.01)f(0)h=0.99009910.01=0.0099010.01=0

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