find and simplify the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h
eq0$ for the given function. $f(x)=-2x^{2}-x - 4$ $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Question

Accepted Answer

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

Answer: