Note the followingI 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.