Question: Let a scalar function be defined as f ( r ) = 3 x 2 3 y 2 3 z 2 - 2 x y

Let a scalar function be defined as f(r)=3x23y23z2-2xy-16x-12z14. The gradient goes to 0 at minima, maxima, and saddle points. This particular f has only a single minimum. By setting gradf=0, solve for the (x,y,z) coordinates that set the gradient to a zero vector. This will be the location of the minimum of f .
Let a scalar function be defined as f ( r ) = 3 x

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