Find the extrema of the given function subject to the given constraint.

a. \(f(x, y)=(x+y)^{2}, x^{2}+y=1\).

b. \(f(x, y)=x^{2} y+x y^{2}, x^{2}+y^{2}=2\).

c. \(f(x, y)=2 x+3 y, 3 x^{2}+2 y^{2}=3\).

d. \(f(x, y, z)=x^{2}+y^{2}+z^{2}, x y z=1\).

e. \(f(x, y, z)=x y+y x, x^{2}+y^{2}=1, x z=1\).