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Chapter 2: Q. 82 (page 70)

In Problems 75– 82, find the difference quotient of f; that is, find f(x+h)-f(x)h,h≠0,for each function. Be sure to simplify.

f(x)=x+1

Short Answer

Expert verified

The value off(x+h)-f(x)h=1x+h+1+x+1

Step by step solution

01

Step 1. Given Information

In this problems we have to find the difference quotient of f; that is, find f(x+h)-f(x)h,h≠0,for given function. Be sure to simplify.

The given function is
f(x)=x+1

02

Step 2. Firstly we find the value of f(x+h)We find the value of f(x+h) by putting x=x+h in given function.

f(x+h)=x+h+1

03

Step 3. Putting the value of f(x) and f(x+h) in the f(x+h)- f(x)h

f(x+h)-f(x)h=x+h+1-x+1h

To rationalize we multiply and divide with x+h+1+x+1

f(x+h)-f(x)h=x+h+1-x+1h·x+h+1+x+1x+h+1+x+1

Using the formula (a2-b2)=(a+b)(a-b)

f(x+h)-f(x)h=x+h+12-x+12h(x+h+1+x+1)f(x+h)-f(x)h=x+h+1-(x+1)h(x+h+1+x+1)f(x+h)-f(x)h=x+h+1-x-1h(x+h+1+x+1)f(x+h)-f(x)h=hh(x+h+1+x+1)f(x+h)-f(x)h=1x+h+1+x+1

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Most popular questions from this chapter

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2+4

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

A wire of length xis bent into the shape of a circle.

Part (a): Express the circumference Cof the circle as a function of x.

Part (b): Express the areaAof the circle as a function ofx.

A wire 10meters long is to be cut into two pieces. One piece will be shaped as a square, and the other piece will be shaped as a circle. See the figure.

Part (a): Express the total area Aenclosed by the pieces of wire as a function of the length x of a side of the square.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Asmallest?

The short-term

(no more than 24hours) parking fee F (in dollars) for

parking x hours at O’Hare International Airport’s main

parking garage can be modeled by the function

role="math" localid="1645828501222" F(x)=2if0<x≤14if1<x≤310if3<x≤45int(x+1)+2if4<x<951if9≤x≤24

Determine the fee for parking in the short-term parking

garage for

(a) 2hours

(b) 7hours

(c) 15hours

(d) 8hours and 24minutes
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