Find the maximum and minimum values of 3x+3y+2z on the sphere x^2+y^2+z^2=1 .
Use of LaGrange Multipliers (maybe?)
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:
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?