Prove that maximum of $\displaystyle sin^2(x)+sin^2(y)+sin^2(z)$ with $\displaystyle x+y+z=180$ is when $\displaystyle x=y=z=60$
This is a function from R^3 -> R. Find the Jacobian, (a 1x3 matrix, gradient). See if (x,y,z) = (60,60,60) is a critical point. then find the Hessian (the matrix of second order partial derivatives.), then use the second partial derivative test.
Last edited by MacstersUndead; Aug 25th 2010 at 08:31 PM.