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