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## Bound between two convex functions [closed]

I'm trying to find the upper bound between two convex functions f(x)-g(x) for x \in [-a, b] where g(x) = cx for x >= 0; (c-1)x for x<0. And f(x) is any convex and differentiable function. Another way to look at the question is that g(x) is not differentiable at x = 0, we can therefore approximate g(x) with f(x) for x \in [-a,b] in the local neighbourhood of x=0. Thanks

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 try math.stackexchange.com/questions – Will Jagy Sep 6 at 19:13