given a tangent line, find f(x)

mbrmbrg

I have a homework problem as follows:

If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4).

Using the slope formula and the point-slope formula, I found that the equation of the given tangent line is y = 1/4x + 2.

Now I want to find f(x) so I can actually answer the question.

I thought I might be able to solve for f(x) using the equation

f'(a)= lim [f(x+h) - f(x)]/h
h-->0

and subsituting 1/4 for f'(a), but I can't get any farther than setting that up.

help? please?
thanks!

daveb

You don't need f(x) to know what f(4) is. You're already given f(4)

mbrmbrg

Thank you!
I have to remember that learning calculus does not mean forgetting the very first rules of reading ordered pairs, don't I...

HallsofIvy

Well put!

accordeonist

what will be f'(4)?

0?