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Calculus inflection point question

  1. Jun 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Suppose that f has a continuous second derivative for all x, and that f(0) = 1, f'(0) = 2, and f''(0) = 0. Does f have an inflection point at x = 0?

    2. Relevant equations

    3. The attempt at a solution
    I know that for f'' to have a point of inflection, it needs to change sign near that point, but I can't remember if there's a test for f'' that involves f' to find out if it does. Should I just say that it is impossible to say, since I can't analyze the 'neighborhood' of x = 0 to see if f'' changes sign?
  2. jcsd
  3. Jun 18, 2010 #2


    Staff: Mentor

    Since f' is continuous for all x, small changes in x correspond to small changes in f'(x). For a value c very close to 0, f'(c) would have to decrease by 2 units in order for it to become negative.
  4. Jun 21, 2010 #3


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