I have the following function(adsbygoogle = window.adsbygoogle || []).push({});

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

where [itex]B[/itex] and [itex]C[/itex] are constants and where [itex]y[/itex] is a monotonically

decreasing function of [itex]x[/itex] ([itex]\mid\frac{dy}{dx}\mid[/itex] stands for absolute value of derivative). According to my model, all

signs indicate that [itex]f[/itex] is a monotonically increasing function of

[itex]x[/itex]. Numerical experiments and logical arguments confirm this but

I need a rigorous proof of this. If [itex]f[/itex] is not unconditionally monotonically

increasing function of [itex]x[/itex] I wish to know under what conditions it

will be monotonically increasing function of [itex]x[/itex].

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# Monotonically increasing function

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