Hi;

I am trying to find the radius of the smallest sphere centered at {2,2,2} that also intersects the surface z = x + 1 using Lagrange Multipliers - see attached notebook. Believing that I have found the correct solution using Lagrange Multipliers and visual methods, I attempted to verify the answer using the Maximize and Minimize functions, and that is where I ran into problems with the Maximize function not seeming to recognize the constraint function and running off to infinity. I then tried to resolve the problem by using the Sphere function as an input to the Minimize and Maximize function and received totally different answers from the Lagrange Multipliers and visual method.

Since using Lagrange Multipliers, Maximize and Minimize functions as well as Mathematica primitives are somewhat new to me, the problems are most probably the result of something that I am doing incorrectly or just do not understand. Any help you could give would be greatly appreciated.

Thanks,
Mitch Sandlin

Attachments:

LagrangeMultipli...nb