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Thread: Differentiable Functions

  1. #1
    Senior Member
    Feb 2008

    Differentiable Functions

    Could someone help me with this question:

    $\displaystyle The\ function\ is\ given\ by$

    $\displaystyle f(x)=x\ for\ 0 \leq x<1$
    $\displaystyle f(x)=1/x^2\ for\ 1 \leq x<2$

    $\displaystyle and\ f(x)=f(x+2)\ for\ all\ x$

    $\displaystyle 1)\ Is\ f(x)\ odd,\ even\ or\ neither.\ Explain?$

    $\displaystyle 2)\ Is\ f(x)\ periodic?\ If\ so\ state\ the\ period.$

    $\displaystyle 3)\ Find\ any\ relevant\ maxima\ or\ minima\ of\ f(x)$
    Last edited by acevipa; Apr 24th 2010 at 03:45 AM.
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  2. #2
    Apr 2010
    odd and even functions have the following properties:

    even F(x)=F(-x)

    odd -F(x)=F(-x)

    the first function in your question is odd, the second is even. Using these fomrulas you can work it out by yourself quite easily.

    a function is periodic when its values repeat itself every now and then. Therefore if we have a function that looks like

    F(x)=F(x+P) it is most certainly a periodic function. P is the period.

    finally minima and maxima. You can see that differentiating these functions will not help here. You do know the limits though and you can easily find for which value the function will have its largest and smallest value.
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