Question

find the difference quotient $\frac{f(x + h)-f(x)}{h}$, where $h
eq0$, for the function below.
$f(x)=-8x + 6$
simplify your answer as much as possible.
$\frac{f(x + h)-f(x)}{h}=square$

Explanation:

Step1: Find $f(x + h)$

Substitute $x+h$ into $f(x)=-8x + 6$. So $f(x + h)=-8(x + h)+6=-8x-8h + 6$.

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

\[

$$\begin{align*} f(x + h)-f(x)&=(-8x-8h + 6)-(-8x + 6)\\ &=-8x-8h + 6 + 8x-6\\ &=-8h \end{align*}$$

\]

Step3: Find the difference - quotient

\[
\frac{f(x + h)-f(x)}{h}=\frac{-8h}{h}=-8
\]

Answer:

$-8$