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Math Help - Concave upward and downward

  1. #1
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    Concave upward and downward

    Find the points of inflection of the graph of the function.
    f(x)= x\sqrt{15-x}

    The second derivative

     f''(x)=\frac{45}{4\sqrt{x}}
    I can see that f''(x) is undefined at 0. There is no points of inflection.

    Then why doesn't the upward concave exist but does the downward concave exist?
    Can anyone help me explain it?
    Last edited by dangbeau; March 25th 2013 at 08:10 AM.
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  2. #2
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    Re: Concave upward and downward

    Quote Originally Posted by dangbeau View Post
    Find the points of inflection of the graph of the function.
    f(x)= x\sqrt{15-x}

    The second derivative

     f''(x)=\frac{45}{4\sqrt{x}}
    I can see that f''(x) is undefined at 0. There is no points of inflection.
    Where did you get that second derivative? Look at this.
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  3. #3
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    Re: Concave upward and downward

    Ah sorry, I also use that website but add inputs wrongly.
    Then this one
    \frac{3(x-20)}{4(15-x)^{\frac{3}{2}}}
    There is no reflection points
    while reading my book, I understand more about it (before that, I thought non-reflection points means non-concave upward and downward >.<)

    So at x=15 f'' is undefined
    Domain: x\leq15
    Plug in 14 to f'' we get negative value=> concave downward

    But I still don't understand why we have to test at the point f'' is undefined?
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