given the function f(x)=1/(11x), find the difference quotient (f(-4 + h)-f(-4))/h

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:

$\frac{1}{44(-4 + h)}$