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I have an expression that I would like to evaluate:

2 phi''[1 + a (-1 + u[10])] phi'[q]^3 > phi''[q] phi'[q] phi'[1 + a (-1 + u[10])]^2

Is there any way of telling Mathematica that the function phi is strictly increasing and convex?

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Could you clarify what you mean by "evaluate"? Have a, u[10], and q been given definite real values or do you want to find combinations of them for which the inequality might be true for some phi? –  whuber May 2 '13 at 14:47
    
Ideally the latter, but I'd be happy I got as far as Mathematica giving me back a True or False when I pin down all three of these things to particular values. –  RoyalTS May 2 '13 at 16:12

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