Find maxima, mimima and saddle points for each of the following func-tions:

a) f(x,y)=6x^2 - 2x^3 + 3y^2 + 6xy

b) f(x,y)=(x^2 + y^2 - 1)^-1

Firstly, is my answer for part a) correct:

df/dx= 12x - 6x^2 + 6y

df/dy= 6y + 6x

found x=0 and x=1 then y=0 and y=-1

so, the critical points are (0,0) and (1.-1)

doing the 'second derivative test' found (0,0) to be a local minimum and (1,-1) to be a saddle point.

Secondly, i am at a total loss of what to do for part b) as its a fraction and i cant seem to use partial fractions to seperate the variables!!?

Thank you x