Given a tangent line, find f(x)

  1. 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!
     
    Last edited: Jul 10, 2006
  2. jcsd
  3. You don't need f(x) to know what f(4) is. You're already given f(4)
     
  4. Thank you!
    I have to remember that learning calculus does not mean forgetting the very first rules of reading ordered pairs, don't I...
     
  5. HallsofIvy

    HallsofIvy 40,767
    Staff Emeritus
    Science Advisor

    Well put! :approve:
     
  6. what will be f'(4)?

    0?
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?