Question

How do you find the original function given a point (a,b) and the equation of the line tangent to the graph of f(x) at (a,b).

For example:
The point is (4,-11) and 7x-3y=61 is the equation of the line tangent to the graph of f(x)

Answer 1

now you have given even less information than in your last post!

There are many many functions passing through (4,-11) tangent to that line. The simplest is, of course,

f(x) = (7x-61)/3

Even the next simplest one could be a parabola opening either up or down, and there are lots of those.

Or, it could be an exponential function, or a logarithmic function, or a sine/cosine.

I'm sure there is something you have still left out.

Answer 2

Actually, I'm looking for f(a) and f'(a), so i know I can just plug in the x value for f(a) which f(4) would equal -11, but how do i find the derivative in this case?