maximunm value.

[stuart clark]

If \(\displaystyle x,y,z\in \mathbb{R}\) and \(\displaystyle x+y+z = 0\) and \(\displaystyle x^2+y^2+z^2 = 6\). Then \(\displaystyle Max.(x^2y+y^2z+z^2x)\)

 

[tkhunny]

Have you considered LaGrange?

\(\displaystyle F(x,y,z,\lambda,\mu) = x^{2}y + y^{2}z + z^{2}x - \lambda(x+y+z) - \mu(x^{2}+y^{2}+z^{2}-6)\)

Find the five partial derivatives, set them all to zero, and have at it! It's fun!!