This was a question on my test yesterday and I was confused on how to do this. Could someone solve this one out for me?
Find a point on the sphere x^2 + y^2 + z^2 = 4 that is the farthest away from point (1,-1,1)
That is you want to maximize the distance from a point on the sphere to this point.
f represents the constraint. That is if ,
Let be a Lagrange multiplier for this problem.
Solve for in , that is to say :