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In each case, find the maximum and minimum values of \( f(x, y) \) subject to the constraint \( g(x, y)=0 \) using the method of Lagrange multipliers. (a) \( f(x, y)=x-y, g(x, y)=1-x^{2}-y^{2} \). (b) \( f(x, y)=x y, g(x, y)=1-x^{2}-4 y^{2} \)

In each case, find the maximum and minimum values of f(x,y) subject to the constraint g(x,y)=0 using the Lagrange multiplier method