Q. 76 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 75– 82, find the difference quotient of $f$; that is, find $\frac{f(x+h)- f\left(x\right)}{h}, h\ne 0,$for each function. Be sure to simplify.

$f\left(x\right)=-3x+1$

Step-by-Step Solution

Answer

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

Step 1. Given Information

In this problems we have to find the difference quotient of $f$; that is, find $\frac{f(x+h)- f\left(x\right)}{h}, h\ne 0,$for given function. Be sure to simplify.

The given function is
$f\left(x\right)=-3x+1$

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.

$$\begin{gathered} f(x+h)=-3(x+h)+1 \\ f(x+h)=-3x-3h+1 \end{gathered}$$

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

$$\begin{gathered} \frac{f(x+h)- f\left(x\right)}{h}=\frac{-3x-3h+1-(-3x+1)}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=\frac{-3x-3h+1+3x-1}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=\frac{-3h}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=-3 \end{gathered}$$