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I'm having a really hard time knowing where to start with this, I'd appreciate if anyone could give me a hand!

Prove or disprove the following statement. The particular function that extremises a certain functional J among all the functions that render l to another functional K also gives an extremum to the functional K among all the functions that give J a precribed value.

Thanks

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    As in: The unit square has minimal circumference among all rectangles of area $1$ and also maximal area among rectangles of circumference $4$.2012-11-22

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