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Chapter 2: Q. 77 (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)=x2-x+4

Short Answer

Expert verified

The value off(x+h)-f(x)h=2x+h-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鈮�0,for given function. Be sure to simplify.

The given function is
f(x)=x2-x+4

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)2-(x+h)+4

Using the formula (a+b)2=a2+2ab+b2

f(x+h)=x2+2xh+h2-x-h+4

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=x2+2xh+h2-x-h+4-(x2-x+4)hf(x+h)-f(x)h=x2+2xh+h2-x-h+4-x2+x-4hf(x+h)-f(x)h=2xh+h2-hhf(x+h)-f(x)h=h(2x+h-1)hf(x+h)-f(x)h=2x+h-1

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