Make a table of values for the function $F(x)=(x+2) /(x-2)$ at the points $x=1.2, x=11 / 10, x=101 / 100, x=1001 / 1000$ $x=10001 / 10000,$ and $x=1 .$

a. Find the average rate of change of $F(x)$ over the intervals $[1, x]$

b. Extending the table if necessary, try to determine the rate of change of $F(x)$ at $x=1 .$

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Use the method in Example 3 to find (a) the slope of the curve at the given point $P,$ and $($ b) an equation of the tangent line at $P .$

\begin{equation}

y=x^{3}-12 x, \quad P(1,-11)

\end{equation}