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Math Help - Monotonically increasing function

  1. #1
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    Monotonically increasing function

    I have the following function

    f=\frac{B}{y^{3}}+\frac{C}{y^{4}}\mid\frac{dy}{dx}  \mid

    where B and C are constants and where y is a monotonically
    decreasing function of x ( \mid\frac{dy}{dx}\mid stands for absolute value of derivative). According to my model, all
    signs indicate that f is a monotonically increasing function of
    x. Numerical experiments and logical arguments confirm this but
    I need a rigorous proof of this. If f is not unconditionally monotonically
    increasing function of x I wish to know under what conditions it
    will be monotonically increasing function of x.
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  2. #2
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    Re: Monotonically increasing function

    y=cosx is monotonically decreasing from 0 to 180.
    y=-sinx
    IyI=sinx which is increasing from 0 to 90 and decreasing from 90 to 180.

    dIyI/dx needs to be positive. For above example,
    dIyI/dx=cosx which is positive from 0 to 90.

    a,b positive: b<a -> b3<a3 & b4<a4
    a,b negative: b<a -> b3<a3 & b4>a4
    Last edited by Hartlw; November 22nd 2013 at 05:02 AM.
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