I'm trying to find the maximum value of the function $f(x,y)=(ax+by)^p+x^p$ subject to the constraint $x^p+y^p=1$. Here, $a,b$ and $p$ are constants with $a,b>0$ and $p>1$, and $x,y>0$. I have found the maximum in the special case $p=2$ and tried to use Lagrange multipliers in the general case but couldn't success. Any help?
2026-04-03 17:49:54.1775238594
A maximization problem
136 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CALCULUS
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