Extrema of Functions of two variables: Find the critical points of the function and from the form of the function determine whether a relative maximum or relative minimum occurs at each point.

f(x,y,z)=x^2+(y-3)^2+(z+1)^2

Question

Extrema of Functions of two variables: Find the critical points of the function and from the form of the function determine whether a relative maximum or relative minimum occurs at each point.

f(x,y,z)=x^2+(y-3)^2+(z+1)^2

anonymous · Answer

I'm confused on how to determine the absolute minimum. I get critical points of (0,3,-1)

anonymous · Answer

and the second derivatives and third derivative for fxy :$$f _{xx}=2,f _{yy}=2,f _{xy}=0$$

anonymous · Answer

Or is the absolute minimum the same as a relative minimum?