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I'm solving a problem of Lagrange multipliers for $f(x,y,z)=Ax+By+Cz$ subject to $x^a y^b z^c=N$ where $a,b,c,A,B,C,N$ are constants

I need to find a smooth manifold in order to use the Lagrange theorem, and for doing this I should find a regular value for $g(x,y,z)=x^a y^b z^c - N$. Which may be a regular value for $g$ or how can I find it?

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