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Math Help - [SOLVED] constant infiniti function

  1. #1
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    [SOLVED] constant infiniti function

    hey guys,have a tough problem....any help would be great

    Let f(x) be C∞ function and assume that ∃a > 0 such that such that f ′(a) f '(2a) < 0. Show that f(x) has a local extrema on (0,∞).

    f ' meaning f prime
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lsanger View Post
    hey guys,have a tough problem....any help would be great

    Let f(x) be C∞ function and assume that ∃a > 0 such that such that f ′(a) f '(2a) < 0. Show that f(x) has a local extrema on (0,∞).

    f ' meaning f prime
    The derivative of f changes sign between a and 2a. But the drivative is continuous, and hence f'(x)=0 for some x \in (a,2a)

    CB
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  3. #3
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    By the way, you titled this "constant infinity function".

    You understand, do you not, that the "C" in C^\infty means continuous, not "constant". Functions in C^\infty are the functions, all of whose derivatives are continuous.
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