follow the step by step process to determine the difference quotient, $\frac{f(x + h)-f(x)}{h}$
f(x)=4x^{2}-3
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. do not factor.)
c. determine the difference quotient $\frac{f(x + h)-f(x)}{h}$
$\frac{f(x + h)-f(x)}{h}=$
(simplify your answer. do not factor.)

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute $x+h$ into $f(x)$:
$$
\begin{align*}
f(x + h)&=4(x + h)^{2}-3\
&=4(x^{2}+2xh+h^{2})-3\
&=4x^{2}+8xh + 4h^{2}-3
\end{align*}
$$
## Step2: Calculate f(x + h) - f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(4x^{2}+8xh + 4h^{2}-3)-(4x^{2}-3)\
&=4x^{2}+8xh + 4h^{2}-3 - 4x^{2}+3\
&=8xh+4h^{2}
\end{align*}
$$
## Step3: Determine the difference quotient $\frac{f(x + h)-f(x)}{h}$
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{8xh + 4h^{2}}{h}\
&=\frac{h(8x + 4h)}{h}\
&=8x+4h
\end{align*}
$$
# Answer:
a. $4x^{2}+8xh + 4h^{2}-3$
b. $8xh+4h^{2}$
c. $8x + 4h$

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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 \(\frac{f(x + h)-f(x)}{h}\)

Answer: