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Math Help - Differentiation

  1. #1
    Junior Member
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    Differentiation

    Hi, I've already proven that dy/dx=1/2{1-(9/[2t^2+1])}

    How do I show that dy/dx<1/2??

    Thanks a lot!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by cyt91 View Post
    Hi, I've already proven that dy/dx=1/2{1-(9/[2t^2+1])}

    How do I show that dy/dx<1/2??

    Thanks a lot!
    Hi cyt91,

    \frac{dy}{dx}=\frac{1}{2}\left[1-\left(\frac{9}{2t^2+1}\right)\right]=\frac{1}{2}\left[\frac{2t^2+1}{2t^2+1}-\frac{9}{2t^2+1}\right]

    =\frac{1}{2}\left[\frac{2t^2+1-9}{2t^2+1}\right]

    and as the numerator of the second factor is clearly less than the denominator, the second factor is less than one,

    hence the overall expression is less than 0.5
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