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Math Help - maximum problem

  1. #1
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    maximum problem

    given f(x)=integration of sin(s^2)ds from 0 to x

    i found out d(f(x))=sin(x^2)

    i am unable to find the maximum for triple derivative of f(x) in interval [pi/2] please help
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  2. #2
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    Re: maximum problem

    so you want the maximum of $\dfrac {d^2}{{dx}^2}\left(\sin(x^2)\right)$ ?

    $\dfrac d {dx}\left(\sin(x^2)\right) = 2x \cos(x^2)$

    $\dfrac d {dx} \left(2x \cos(x^2)\right) = 2\cos(x^2) - 4x^2\sin(x^2)$

    Taking a quick look at this on $0 \leq x \leq \dfrac {\pi} 2$

    maximum problem-clipboard01.jpg

    You can see that it looks like the maximum is at $x=0$

    Checking for roots of $2\cos(x^2) - 4x^2\sin(x^2)=0$ we find

    $x=0, x\approx 1.47466$

    The second root is a minimum and so the maximum on this interval is at $x=0$
    Thanks from prasum
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  3. #3
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    Re: maximum problem

    thanks
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