find an equation of the tangent line to the graph of the function f through the point (xsub0, ysub0) not on the graph. TO find the point of tangency (x,y) on the graph of f, solve the equation ....

Answer 1

It is not always possible to find such a tangent line.

Consider the graph of y=x^2. No tangent line will pass through the point (0,1), since it lies inside the parabola.

However, assuming that the point is properly placed, we need to find a point (x,y) on the graph such that the tangent line passes through (x,y) and (x0,y0).

That is, f'(x) = (y0-y)/(x0-x)