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If f(2) = 3 and f ' (2) = -1, then what is f(x)

  1. Jan 5, 2008 #1
    This is more of a generic question...but it's shown up in so many of my homework questions that I thought I would consult the pros at PF.

    If I am given...let's say:

    f(2) = 3
    f'(2)= -1

    How would I go about finding f(x)

    Thanks in advance. :rolleyes:
     
  2. jcsd
  3. Jan 5, 2008 #2

    rock.freak667

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    Homework Helper

    ...integration is the reverse of differentiation...

    i.e. [tex]\int f'(x) dx=f(x)+C[/tex]
     
  4. Jan 5, 2008 #3
    Knowing the value of the function and its derivative at only one point (x=2) tells you nothing about the behavior of the function anywhere else, so no, you can't find f(x) just from those two pieces of information. In other words, f could be a straight line, a parabola, an infinite polynomial series, etc.
     
  5. Jan 5, 2008 #4
    Thanks for the fast replies!

    I haven't learned integration yet.

    So then how do you propose I do this question. (Actual HW question)

    Given:
    g(2) = 3
    g'(2) = -2
    h(2) = -1
    h'(2) = 4

    f(x) = g(x)/h(x)

    Find f'(2)
     
  6. Jan 5, 2008 #5

    rock.freak667

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    Use the quotient rule to find f'(x) and then sub x=2.Then sub the values that you were given.
     
  7. Jan 5, 2008 #6
    Try differentiating f(x). You should get a result in terms of g, g', h, and h'. Plug in and you're done. :)
     
  8. Jan 5, 2008 #7
    Genius! Thanks :D
     
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