Question

The function g(x,y) = x^4+y^3 has a critical point at (0,0). What sort of critical point is it?

Answer 1

its either a min, a max, or a saddle that is a min of one and a max of the other id assume

Answer 2

gx = 4x^3
gxx = 12x^2
gxy = 0

gy = 3y^2
gyy = 3y
gyx = 0

Answer 3

The second derivative test fails but i there is another method the has something to do with completing the square

Answer 4

if we graph the projections into the zx and zy planes we can see that its a min

Answer 5

err, something close to a min :)