Calculus
posted by Olivia .
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 7x3y=61 is the equation of the line tangent to the graph of f(x)

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) = (7x61)/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. 
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?