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Chapter 2: Q. 76 (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)=-3x+1

Short Answer

Expert verified

The value off(x+h)-f(x)h=-3

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)=-3x+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)=-3(x+h)+1f(x+h)=-3x-3h+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=-3x-3h+1-(-3x+1)hf(x+h)-f(x)h=-3x-3h+1+3x-1hf(x+h)-f(x)h=-3hhf(x+h)-f(x)h=-3

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