Based on a coordinate system centered in a sphere where is $M(x, y, z) = 6x - y^2 + xz + 60$ smallest? I am trying to work through a few examples in my workbook, and this one has me completely dumbfounded. 
Suppose I have a sphere of radius 6 metres, based on a coordinate system centred in that sphere, at what point on the sphere will $M(x, y, z) = 6x - y^2 + xz + 60$ be smallest?
I have been racking my brain for ages, but I don't see how best to solve this.
If someone has any ideas, I would greatly appreciate your help.
Cheers
Tim

On your sphere $x^2+y^2+z^2=6^2$, so that $y^2=\ldots$. Substitute this into $M$ to have a function of $x$ and $z$ only.
