1. The problem statement, all variables and given/known data Find the maximum and minimum values of 3x+3y+2z on the sphere x^2+y^2+z^2=1 . 2. Relevant equations Use of LaGrange Multipliers (maybe?) 3. The attempt at a solution I have no idea if LaGrange multipliers is the way to go or not, but I took the partial derivative for x, y and z Partial x = 3 Partial y = 3 Partial z = 2 Using LaGrange Multipliers I then got the following equations: 3=lambda2x 3=lambda2y 2=lambda2z Lambda being the LaGrange Multiplier I believe. I also have the equation of the sphere or x^2+y^2+z^2=1 However, from here I had no idea where to go next. I tried to solve out the LaGrange Formulas but couldn't get a coherent answer. Am I on the right track or do I need to just forget LaGrange?