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how can I proof this:

given: a convex function on an open interval I,which is a subset of R.

I have to show that the function can be differentiated on the whole interval.

I already proved the following for a<b<c, a,b,c in I:

f(b)-f(a))/(b-a)<(f(c)-f(a))/(c-a)<(f(c)-f(b))/(c-b).

Thanks for help!

Jonas

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# Convex function

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