Locate and Classify All Critical Points for the Given Function $f(x, y)=e^{\left(x^{2}+y^{2}\right)}$

Multiple Choice

Locate and classify all critical points for the given function.
- $f(x, y) =e^{\left(x^{2}+y^{2}\right) }$

A) Maximum of 1 at $(0,0)$
B) Maximum of 0 at $(0,0)$
C) Minimum of 0 at $(0,0)$
D) Minimum of 1 at $(0,0)$