Science:Math Exam Resources/Courses/MATH100 C/December 2024/Question 10 (a)/Solution 1

Following the definition of the critical point we compute the following derivatives:

$$f_x=y,\text{and}{f}_y=x.$$

Both $f_x$, and $f_y$ are defined everywhere on the domain, so the only critical point occurs when the derivative is zero, which is at $(0,0)$.