- #1
JulieK
- 50
- 0
I have the following function
[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].
[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].