Let $f(x) = \frac{1}{x-2}$. Calculate the difference quotient
$\frac{f(-2+h)-f(-2)}{h}$ for
$h=.1$
$h=.01$
$h=-.01$
$h=-.1$
If someone now told you that the derivative (slope of the tangent line to the graph) of $f(x)$ at $x=-2$ was $-1/n^2$ for some integer $n$ what would you expect $n$ to be?
$n=$