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Intro to Derivative Questions

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data
    If the functions f and g are defined so that f'(x) = g'(x) for all real numbers x with f(1)=2 and g(1)=3, then the graph of f ad the graph of g:

    Is the answer that they do not intersect?
    The other choices are:
    • intersect exactly 1 time
    • intersect no more than 1 time
    • could intersect more than 1 time
    • have a common tangent at each pt. of tangency.
    How would I be able to prove this?

    #2)
    If the function g is differentiable at the point (a, g(a)), then which of the following are true?

    g'(a) = lim g(a+h) - f(a)
    h
    g'(a) = lim g(a)-g(a-h)
    h
    g'(a) = lim g(a+h)-g(a-h)
    h

    I think that it is only the first one can be correct. Can any of the others be correct?

    (Above, the h is on the end, but the h should be under the numerator.
     
  2. jcsd
  3. Oct 12, 2009 #2

    LCKurtz

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    1. Think about the function h(x) = f(x) - g(x). What can you say about h?
     
  4. Oct 12, 2009 #3
    I'm assuming that #2 limits are taken as h -> 0, and that the first option should have g(a) in it, not f(a). To answer this question, all you need to know is the definition of the derivative.
     
  5. Oct 12, 2009 #4
    Yes, it is the limits as h approaches 0. I made an error however, would the 3rd equation in E2 be correct if there is a 2h in the denominator?
     
  6. Oct 12, 2009 #5
    What about the first option? Is that f(a) supposed to be there? Once again, you need to know the definition of the derivative.
     
  7. Oct 12, 2009 #6
    Yea I think it is supposed to be f(a).
     
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