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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.

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How can I prove that the following function is increasing according to x1?

Suppose that $0 \le {X_1} < {X_2} < {X_3}$ . How is it possible to prove the following function is increasing based on ${X_1}$ in the range of $0 \le {X_1} < {X_2}$ ? $f({X_1},{X_2},{X_3}) = \frac …
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