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## Homework Statement

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

1) f(x,y)=x

^{2}y+xy

^{2}

2)f(x,y) = x

^{4}+2*x

^{3}y+x

^{2}y

^{2}+y

^{4}

## 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?