follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$. f(x)=6 - 8x^2 a. determine f(x + h). f(x + h)= (simplify your answer.) b. simplify the expression f(x + h)-f(x). f(x + h)-f(x)= (simplify your answer.) c. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$. $\frac{f(x + h)-f(x)}{h}=$ (simplify your answer.)

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute $x+h$ into $f(x)=6 - 8x^{2}$.
$$
\begin{align*}
f(x + h)&=6-8(x + h)^{2}\
&=6-8(x^{2}+2xh+h^{2})\
&=6-8x^{2}-16xh - 8h^{2}
\end{align*}
$$
## Step2: Calculate f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(6-8x^{2}-16xh - 8h^{2})-(6 - 8x^{2})\
&=6-8x^{2}-16xh - 8h^{2}-6 + 8x^{2}\
&=-16xh-8h^{2}
\end{align*}
$$
## Step3: Determine the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{-16xh-8h^{2}}{h}\
&=\frac{h(-16x - 8h)}{h}\
&=-16x-8h
\end{align*}
$$
# Answer:
a. $6-8x^{2}-16xh - 8h^{2}$
b. $-16xh-8h^{2}$
c. $-16x - 8h$

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QUESTION IMAGE

Question

Explanation:

Step1: Find f(x + h)

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

Step3: Determine the difference quotient

Answer: