Chapter 2.1, Problem 76AYU

To determine

To find the difference quotient $\frac{f\left(x+h\right)-f\left(x\right)}{h}$ .

Answer to Problem 76AYU

  $\frac{f\left(x+h\right)-f\left(x\right)}{h}=-3$

Explanation of Solution

Given:

A function is given as

  $f\left(x\right)=-3x+1$

Calculation:

Difference quotient can be calculated as shown below:

  $\begin{array}{l}\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{\left[-3\left(x+h\right)+1\right]-\left[-3x+1\right]}{h}\\ =\frac{-3x-3h+1+3x-1}{h}\\ =\frac{-3h}{h}\\ =-3\end{array}$

Therefore, the difference quotient is $-3$ .