Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h $
eq$ 0, for the following function. f(x)=3x + 2 $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x):
$f(x + h)=3(x + h)+2=3x+3h + 2$

Step2: Calculate f(x + h) - f(x)

$f(x + h)-f(x)=(3x + 3h+2)-(3x + 2)=3x+3h + 2-3x - 2=3h$

Step3: Find the difference quotient

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

Answer:

3