1. The problem statement, all variables and given/known data Using Lagrange Multipliers, we are to find the maximum and minimum values of f(x,y) subject to the given constraint 2. Relevant equations f(x,y,z) = x^2 - 2y + 2z^2, constraint: x^2 + y^2 + z^2 = 1 3. The attempt at a solution grad f = lambda*grad g (2x, -2, 4z) = lambda(2x, 2y, 2z) therefore: 2x = lambda2x -2 = lambda2y 4z = lambda2z Now i can see how x and z can both equal 0, and how lambda can equal 1, and how y eventually equals -1 and f(0,-1,0)=2, yet in the solutions there is another part to it where it says OR, Lambda = 2, y = -1/2, x = 0, z= +- sqrt(3)/2. <---i do not have any idea how these values came to be, no idea at all. Any help would be appreciated, thanks.