Given $f(x)=\frac{1}{x}$, complete the following problems.

1. Compute the average rate of change from $x = 2$ to $x = 3$.

   Step (a):

   $\frac{f(3)-f(2)}{3-2}$

2. Show that the average rate of change from $2$ to $2 + h$ is $\frac { - 1 } { 2 ( 2 + h ) }$.

   Step (b):

   $\frac{f(2+h)-f(2)}{2+h-2}$

3. Show that the average rate of change from $x$ to $x + h$ is $\frac { - 1 } { x ( x + h ) }$.

   Step (c):

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

4. What is the $\lim \limits _ { h \rightarrow 0 } \frac { - 1 } { x ( x + h ) }$?

   Hint (d):

   Substitute $0$ in for $h$.