I have the following function:

and I know that there is a critical point at

. I have been asked to determined the type of critical point. The second derivatives give no information, and I'm not supposed to consider higher derivatives.

"Obviously" it is a minimum point, so I thought it would be enough to show that

near

.

By introducing polar coordinates I got:

.

Since

, it should be enough to show that

, but I seem unable to do it. Does this seem like the right method, and if so, does anyone know how to go on from here?

Another thought I had was to compare with

or

, but that didn't get me anywhere.

Aliquantus