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Math Help - Derivatives and Second Derivatives

  1. #1
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    Derivatives and Second Derivatives

    A function f satisfies the following conditions...
    f(4) = 28
    f '(4) = 3
    f ''(x) < 0 for x >or= 4

    Which of the following are possible values for f(6)? (Select all that apply.)
    a. 31
    b. 34
    c. 37
    d. None of these
    Last edited by melliep; September 23rd 2010 at 10:35 PM.
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  2. #2
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    Quote Originally Posted by melliep View Post
    f ''(x) < 0 for x 4
    For x\;\;?\;\;4? Something is missing here.
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  3. #3
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    And if someone does reply, could you please tell me why you got the answer you did?

    Thank you.
    Last edited by melliep; September 23rd 2010 at 10:56 PM.
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  4. #4
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    Unless you are missing some more information, they all seem possible (except of course d). The local behavior of a function over \mathbb{R} does not determine its global behavior (this is different for a holomorphic complex functions).

    So the answer is that f(6) could be anything.
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  5. #5
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    Good point but not quite correct. We are given some "global" information- we are told that f"(x) < 0 for all x> 4. Therefore f' is less than 3 for x> 4 and so the graph of f(x) is below the tangent line at x= 4. That tangent line is y= 3(x- 4)+ 28 and when x= 6 that gives 6+ 28= 34. f(6) must be less than 34.
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    Good point but not quite correct. We are given some "global" information- we are told that f"(x) < 0 for all x> 4.
    Yes, thank you of course you are right. I seem to have mis-read the post.
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