# Best simple exponential estimator

Given smooth enough positive $f(x)$. Find real $c$ such that $$\int_0^1 (e^{cx}-f(x))^2dx$$ is minimized.

Note: it only looks innocent..

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How do you anticipate this being answered? It feels like more information is needed. –  Bennett Gardiner Sep 8 '13 at 6:39
Any additional assumption on $f$? For example, if $f=0$ there is no minimizer (the infimum is $0$, "attained" at $-\infty$). –  Etienne Sep 8 '13 at 7:02
I'd like to have $c$ depends on $f$ (or its integrals etc.). Note that $f$ can be negative. For simplicity one can assume positivity. –  Troy McClure Sep 8 '13 at 7:28