the expression (\frac{f(x + h)-f(x)}{h}) for (h
eq0) is called the difference quotient. find and simplify the difference quotient for the following function. (f(x)=3x^{2}+10x + 10). the difference quotient is (simplify your answer.)

Question

the expression (\frac{f(x + h)-f(x)}{h}) for (h
eq0) is called the difference quotient. find and simplify the difference quotient for the following function. (f(x)=3x^{2}+10x + 10). the difference quotient is  (simplify your answer.)

Accepted Answer

# Explanation:
## Step1: Find f(x + h)
Substitute x + h into f(x):
$$
\begin{align*}
f(x + h)&=3(x + h)^2+10(x + h)+10\
&=3(x^{2}+2xh+h^{2})+10x + 10h+10\
&=3x^{2}+6xh+3h^{2}+10x + 10h+10
\end{align*}
$$
## Step2: Calculate f(x + h)-f(x)
$$
\begin{align*}
f(x + h)-f(x)&=(3x^{2}+6xh+3h^{2}+10x + 10h+10)-(3x^{2}+10x + 10)\
&=3x^{2}+6xh+3h^{2}+10x + 10h+10 - 3x^{2}-10x - 10\
&=6xh+3h^{2}+10h
\end{align*}
$$
## Step3: Calculate the difference - quotient
$$
\begin{align*}
\frac{f(x + h)-f(x)}{h}&=\frac{6xh+3h^{2}+10h}{h}\
&=\frac{h(6x + 3h+10)}{h}\
&=6x + 3h+10
\end{align*}
$$
# Answer:
$6x + 3h+10$

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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: