1.For the function z=f(xy)=x^3 -3xy-y^3

a.Find the equation of this function when is fixed at the following values: -2,-1,0,1,2. Plot these equations on the same axes, carefully labelling each line.

b.Find the equation of this function when is fixed at the following values: -2,-1,0,1,2. Plot these equations on the same axes, (though different from the one in part a.) carefully labelling each line.

c.Find fxand fyFor both fx=0 and fy=0plot the relationship between and on the - axis.

d.Find the critical points of the original function .

e.Use the Hessian matrix to check whether these points are local maxima, local minima, saddle points, or whether you can't tell.

Comment on your answers in part d. and e. with regards to what you found in a., b., and c.