find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h ≠ 0, for the following function. be sure to simplify. f(x)=x² - 5x + 6 $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Question

Accepted Answer

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

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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: