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I have a function f(t), and I want to find 2nd order polynomials that lower/upper bound f(t) in a fixed interval. For instance,

f(t) = exp(2t), 0.1<t<0.4

Find a,b,c so that g(t) = a + b t +c t^2 <f(t) for the given interval

I have been googling for the solution, but apparently no one cares about this problem, although I was expecting it to be already solved :( Anyone could give me a reference to look at? Books, papers, whatever.. Oh, by the way, f(t) does not have to be convex.

Thanks a lot!!

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# Quadratic lower/upper bound of a function

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