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If $q>p>0$ show that the point $(x,y)=(0,0$) minimizes the function $$f(x,y)=(y−px2)(y−qx2)$$ locally on the lines $y=ht,x=kt$ through the point $(x,y)$.

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closed as off topic by David Roberts, HenrikRüping, Deane Yang, Gjergji Zaimi, Noah Stein May 30 at 14:16

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