Question

How do you use the limit definition to find the slope of the tangent line to the graph `F(x) = ((12) / (x - 9))` at (3,2)?

Answer 1

There is an error in the question. The point `(3,2)` is not on the graph of this function. So there is no tangent line to the graph at that point.

Explanation:

Assuming that the question should read:

Find the slope of the line tangent to the graph of `F(x) = 12/(x-9)` at `(3,-2)`

`F'(x) = lim_(hrarr0)(F(3+h)-F(3))/h`

`= lim_(hrarr0)(12/(3+h-9) - 12/(3-9))/h`

`= lim_(hrarr0)((12(-6) - 12(-6+h))/((-6)(-6+h)))/h`

`= lim_(hrarr0)(-12h)/((-6)(-6+h)h)`

`= lim_(hrarr0)(-12)/((-6)(-6+h))`

`= (-12)/((-6+0)(-6)) = -1/3`