About the functionals $J(y)=\int_0^1y'(x)dx$ and $K(y)=\int_0^1y^2(x)dx$ on the space of functions $y$ in $C^1([0,1])$ such that $y(0)=0$ and $y(1)=1$

score 40 · Answer 15 · 2026-04-12 22:28:27

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Find $f$ that solves the following optimization problem: $\min_{f} \frac{f(x, y)}{f(y, x) \times x}$, where $x$, $y$ are constant real numbers.

Published on 12 Apr 2026 - 22:28

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About the functionals $J(y)=\int_0^1y'(x)dx$ and $K(y)=\int_0^1y^2(x)dx$ on the space of functions $y$ in $C^1([0,1])$ such that $y(0)=0$ and $y(1)=1$

Find $f$ that solves the following optimization problem: $\min_{f} \frac{f(x, y)}{f(y, x) \times x}$, where $x$, $y$ are constant real numbers.

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