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Chapter 2: Q. 81 (page 70)

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

f(x)=x

Short Answer

Expert verified

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

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鈮�0,for given function. Be sure to simplify.

The given function is
f(x)=x

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

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-xh

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

f(x+h)-f(x)h=x+h-xh路x+h+xx+h+x

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

f(x+h)-f(x)h=x+h2-x2h(x+h+x)f(x+h)-f(x)h=x+h-xh(x+h+x)f(x+h)-f(x)h=hh(x+h+x)f(x+h)-f(x)h=1x+h+x

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