find the difference quotient $ \frac { f ( x + h ) - f ( x ) } { h } $, where $ h \
eq 0 $, for the function below.
$ f ( x ) = 3 x ^ { 2 } - 5 x + 2 $
simplify your answer as much as possible.
$ \frac { f ( x + h ) - f ( x ) } { h } = $

Question

Accepted Answer

# Explanation:
## Step1: Find $ f(x + h) $
Substitute $ x+h $ into $ f(x)=3x^{2}-5x + 2 $.
$$
\begin{align*}
f(x + h)&=3(x + h)^{2}-5(x + h)+2\
&=3(x^{2}+2xh+h^{2})-5x-5h + 2\
&=3x^{2}+6xh+3h^{2}-5x-5h + 2
\end{align*}
$$
## Step2: Calculate $ f(x + h)-f(x) $
$$
\begin{align*}
f(x + h)-f(x)&=(3x^{2}+6xh+3h^{2}-5x-5h + 2)-(3x^{2}-5x + 2)\
&=3x^{2}+6xh+3h^{2}-5x-5h + 2-3x^{2}+5x - 2\
&=6xh+3h^{2}-5h
\end{align*}
$$
## Step3: Find the difference quotient $\frac{f(x + h)-f(x)}{h}$
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{6xh+3h^{2}-5h}{h}\
&=\frac{h(6x + 3h-5)}{h}\
&=6x+3h - 5
\end{align*}
$$

# Answer:
$6x + 3h-5$

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QUESTION IMAGE

Question

Explanation:

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

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

Step3: Find the difference quotient \(\frac{f(x + h)-f(x)}{h}\)

Answer: