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## Small proof on monotonic functions

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.

Suppose that $f(x)$ and $g(x)$ are both real-valued differentiable functions defined for all x.

It is known that:
$f'(x)>0$ for all x
$g'(x)>0$ for all x
There exists exactly one value of $c$ such that $f(c) = g(c)$
There exists a $d$ such that $f(d) = g(d)-5$

Prove that $d<c$

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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