For a function S (x, y), if Sz(x, y) = -2xe", Sy(I, V) = (2y + 32 -12) 60 fer(x, y) = -2e", fry(1, y) = -2ce", Sup(x, y) = (2+Ayty?-12) ev then, (a) (0,0) is a local maximum (b) (0, -2) is a local maximum (c) (1.0) is a local minimum (d) (0, -3) is a saddle point (e) (0.0) is a local minimum