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Thread: Which is max min

  1. #1
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    Which is max min

    If $\displaystyle f(1)=4,f(2)=5,\ f(7)=5,\ f(8)=4$, find the value of $\displaystyle f(6)$. also obtain the value of $\displaystyle x$ for which $\displaystyle f(x) $ is maximum or minimum
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  2. #2
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    Quote Originally Posted by zorro View Post
    If $\displaystyle f(1)=4,f(2)=5,\ f(7)=5,\ f(8)=4$, find the value of $\displaystyle f(6)$. also obtain the value of $\displaystyle x$ for which $\displaystyle f(x) $ is maximum or minimum
    There is insufficient information on $\displaystyle f$ to do anything useful with this.

    You could assume assume a quadratic form for $\displaystyle f$, then fit it to the data. As the data is symetric about $\displaystyle x=4.5$, $\displaystyle f$ would then be of the form:

    $\displaystyle f(x)=k(x-4.5)^2+b$

    Now determine $\displaystyle k$ and $\displaystyle b$ from the given data.

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