find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, $h
eq0$, for the following function. $f(x)=2x^{2}-x - 1$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Question

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute x + h into f(x):
$$
\begin{align*}
f(x + h)&=2(x + h)^2-(x + h)-1\
&=2(x^{2}+2xh+h^{2})-x - h-1\
&=2x^{2}+4xh+2h^{2}-x - h-1
\end{align*}
$$
## Step2: Calculate f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(2x^{2}+4xh+2h^{2}-x - h-1)-(2x^{2}-x - 1)\
&=2x^{2}+4xh+2h^{2}-x - h-1 - 2x^{2}+x + 1\
&=4xh+2h^{2}-h
\end{align*}
$$
## Step3: Find the difference quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{4xh+2h^{2}-h}{h}\
&=\frac{h(4x + 2h-1)}{h}\
&=4x+2h - 1
\end{align*}
$$
# Answer:
$4x + 2h-1$

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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

Answer: