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)=4x + 1
$\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute x + h into f(x):
$f(x + h)=4(x + h)+1=4x+4h + 1$

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

$f(x + h)-f(x)=(4x + 4h+1)-(4x + 1)$
$=4x+4h + 1-4x - 1=4h$

Step3: Find the difference quotient

$\frac{f(x + h)-f(x)}{h}=\frac{4h}{h}$
Since $h
eq0$, we can cancel out h:
$\frac{4h}{h}=4$

Answer:

4