I actually made this question up while studying some chemistry. The problem is easy to visualize, but I'm trying to formalize to help myself think more rigorously. To be precise I sort of thought about how you could prove that a reduction in vapor pressure causes a depression freezing point in an ideal solution.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose that [itex]f(x)[/itex] and [itex]g(x)[/itex] are both real-valued differentiable functions defined for all x.

It is known that:

[itex]f'(x)>0[/itex] for all x

[itex]g'(x)>0[/itex] for all x

There existsexactly one value of[itex]c[/itex] such that [itex]f(c) = g(c) [/itex]

There exists a [itex]d[/itex] such that [itex]f(d) = g(d)-5 [/itex]

Prove that [itex]d<c [/itex]

I will be very thankful if someone could help me out. Again this is a problem I made up from my studies in chemistry. Not a homework problem.

Thanks!

BiP

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# Small proof on monotonic functions

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