given the function f(x)=1/(11x), find the dif...
given the function f(x)=1/(11x), find the difference quotient (f(-4 + h)-f(-4))/h
Answer
# Explanation:
## Step1: Find $f(-4 + h)$
Substitute $x=-4 + h$ into $f(x)=\frac{1}{11x}$, we get $f(-4 + h)=\frac{1}{11(-4 + h)}$.
## Step2: Find $f(-4)$
Substitute $x = - 4$ into $f(x)=\frac{1}{11x}$, we get $f(-4)=\frac{1}{11\times(-4)}=-\frac{1}{44}$.
## Step3: Calculate $f(-4 + h)-f(-4)$
\[
\begin{align*}
f(-4 + h)-f(-4)&=\frac{1}{11(-4 + h)}-\left(-\frac{1}{44}\right)\\
&=\frac{1}{11(-4 + h)}+\frac{1}{44}\\
&=\frac{4+( - 4 + h)}{44(-4 + h)}\\
&=\frac{h}{44(-4 + h)}
\end{align*}
\]
## Step4: Calculate the difference - quotient
\[
\begin{align*}
\frac{f(-4 + h)-f(-4)}{h}&=\frac{\frac{h}{44(-4 + h)}}{h}\\
&=\frac{h}{44(-4 + h)}\times\frac{1}{h}\\
&=\frac{1}{44(-4 + h)}
\end{align*}
\]
# Answer:
$\frac{1}{44(-4 + h)}$