Each of the functions f have a critical point at (0,0), however at this point the second derivatives are all zero. Determine te type of critical point at (0,0) in this case
2)f(x,y) = x4+2*x3y+x2y2+y4
The Attempt at a Solution
For the first part by plotting it on Wofram I saw that it was a saddle, and i substituted the values x=y and x=-y to show that there is a saddle point in one direction and a straight line in the other, hence a saddle point, is this sufficient
On 2) I know I must use taylors expansion, but up to how many terms, and what do I do once i get there?