if-F-x-y-F-y-x-and-x-y-c-constant-prove-that-F-max-or-min-F-c-2-c-2-

Question Number 57480 by mr W last updated on 05/Apr/19

$${if}\:{F}\left({x},{y}\right)={F}\left({y},{x}\right)\:{and}\:{x}+{y}={c}\:\left({constant}\right) \\ $$$${prove}\:{that}\:{F}_{{max}\:{or}\:{min}} ={F}\left(\frac{{c}}{\mathrm{2}},\frac{{c}}{\mathrm{2}}\right). \\ $$

Commented by tanmay.chaudhury50@gmail.com last updated on 07/Apr/19

$${what}\:{is}\:{the}\:{difference}\:{between}\:{F}\left({x},{y}\right)\:{and}\:{F}\left({y},{x}\right) \\ $$

Commented by mr W last updated on 07/Apr/19

$${e}.{g}. \\ $$$${F}\left({x},{y}\right)=\mathrm{sin}\:\left({x}\right)\:×\:\mathrm{sin}\:\left({y}\right) \\ $$$${F}\left({y},{x}\right)=\mathrm{sin}\:\left({y}\right)\:×\:\mathrm{sin}\:\left({x}\right)={F}\left({x},{y}\right) \\ $$

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