1. The problem statement, all variables and given/known data Say that P is a point on the surface xyz=8. Is it true or false that you can always find another point Q on the surface such that Q is further away from the origin than P is? 2. Relevant equations ∇f(x,y,z)=λ∇g(x,y,z) where ∇g=0 3. The attempt at a solution Let f(x,y,z)=x2+y2+z2 and g(x,y,z)=xyz-8 Then the ∇f(x,y,z)=λ 2x=λ 2y=λ 2z=λ Therefore x=y=z and then plugging into xyz=8 x3=8 x=2 But then the point (2,2,2) is only the square root of 12 away from the origin, where a point like (8,1,1) is the square root of 66 away from the origin. So I think I minimized the distance instead of maximizing the distance fro the origin, but how do I maximize the distance?