Final Answer:
The function
has no points where both
and
are equal to zero simultaneously.
Explanation:
To find the critical points where both partial derivatives are zero, we compute



Setting both equations to zero to find critical points:

From the first equation,
. Substituting this into the second equation gives

Simplifying, we get
This implies

The value
yields
from
, giving a point (0, 0).
For
, there are no real solutions within the domain.
Hence, the function
has only one critical point at (0, 0), where neither
are zero. This implies that there are no points where both partial derivatives are zero simultaneously.