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Given a,b,c>0 and a+b+c=3
Prove that :[tex] (a+b^{2})(b+c^{2})(c+a^{2}) \leq 13[/tex]
Prove that :[tex] (a+b^{2})(b+c^{2})(c+a^{2}) \leq 13[/tex]
[tex] (b+c^2)(c+a^2) + 2a(a+b^2)(b+c^2) + \lambda = 0 [/tex]They are? What do you think they should be then?
Because there is a constraint. Even if the function does not have a maximum in the region { a,b,c > 0 }, it may have a maximum in { a,b,c > 0 and a+b+c = 3 }. Of course you can get rid of the constraint by eliminating one of the variables (say a), and instead look for extrema ofWhy invoke lagrange multipliers to show that some function doesn't have a local maximum?