We have a local minimum at $(0,0)$. The mechanical way to determine this is to find where the the derivative is $0$ and apply the second partial derivative test.

However, if we sketch the surface $\{(x,y,z)\in \mathbb R^3: z=x^2+y^2\}$ we see that we have a paraboloid that is opening upward and it becomes obvious that $(0,0)$ is a local minimum.

How to find all local extrema using multi-variate calculus
I need to synchronize records, say a list of clients, between a local and distant database. The database on both sides has the same structure. I've thought of using some kind of marker (date field, hash/checksum on field values...) but what would you advise ?

Edit: Distant database is on web hosting so PHP will be needed for transferring data.
