Find the stationary points and local extreme values.

f(x,y) = x^2 +kxy +y^2, k a constant

a) Show that f has a stationary point at (0,0) no matter values is assigned to k.

b) For what values of k will f have a saddle point at (0,0)?

c) For what values of k will f have a local minimum at (0,0)?

d) For what values of k is the second-derivative test inconclusive?