hw9 the derivative as a function (targets l6, d1, d2; §3.2) score: 4/9 answered: 4/9 question 5 for the function f(x)=3x² + 3, evaluate the following, enter your answers in simplest form: f(x + h)= f(x + h)-f(x)= (f(x + h)-f(x))/h= question help: message instructor

Question

Accepted Answer

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

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QUESTION IMAGE

Question

Explanation:

Step1: Find $f(x + h)$

Step2: Find $f(x + h)-f(x)$

Step3: Find $\frac{f(x + h)-f(x)}{h}$

Answer: