Hvordan settes Lagrange-funksjonen opp for to variabler?
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Maks f(x,y)f(x,y)f(x,y) gitt g(x,y)=cg(x,y)=cg(x,y)=c: L(x,y,λ)=f(x,y)−λ(g(x,y)−c)\mathcal{L}(x,y,\lambda)=f(x,y)-\lambda(g(x,y)-c)L(x,y,λ)=f(x,y)−λ(g(x,y)−c). Tre likninger: Lx=fx−λgx=0\mathcal{L}_x=f_x-\lambda g_x=0Lx=fx−λgx=0, Ly=fy−λgy=0\mathcal{L}_y=f_y-\lambda g_y=0Ly=fy−λgy=0, Lλ=−(g(x,y)−c)=0\mathcal{L}_\lambda=-(g(x,y)-c)=0Lλ=−(g(x,y)−c)=0.
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