Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h\
eq0$, for the following function.
$f(x)=4x + 4$
$\frac{f(x + h)-f(x)}{h}=\square$ (simplify your answer.)

Explanation:

Step1: Find \( f(x + h) \)

Substitute \( x+h \) into \( f(x)=4x + 4 \).
\( f(x + h)=4(x + h)+4=4x+4h + 4 \)

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

\( f(x + h)-f(x)=(4x + 4h+4)-(4x + 4) \)
\( =4x+4h + 4-4x - 4 \)
\( =4h \)

Step3: Compute \( \frac{f(x + h)-f(x)}{h} \)

Since \( f(x + h)-f(x)=4h \), then \( \frac{f(x + h)-f(x)}{h}=\frac{4h}{h} \) (where \( h
eq0 \))
\( =4 \)

Answer:

\( 4 \)