Hello,

My question is :

Show that the function

has a saddle point at and find the second derivative along a path through that point has the greatest positive and negative values.

My thoughts:

If I substitute y = x into the function as thus and then find the second derivative as thus this is repeated for the path y = -x as thus with a second derivative of

This is repeated for paths x=y and x=-y giving a derivative of and repectively. So the greatest positive and negative values are 2 and -2. At y=0 and x = 0 the function is constant.

Any Help would be greatly appreciated.

Thank you,

Riptorn70.