Find the Indicated Maxima or Minima $f(x, y)=x^{2}+y^{2}$ , Subject To $x+y=1$

Multiple Choice

Find the indicated maxima or minima.
-Minimum of $f(x, y) =x^{2}+y^{2}$ , subject to $x+y=1$

A) $\frac{1}{2}$ when $x=0, y=1$
B) $\frac{1}{2}$ when $x=\frac{1}{2}, y=\frac{1}{2}$
C) 1 when $x=0, y=1$
D) 1 when $\mathrm{x}=\frac{1}{2}, \mathrm{y}=\frac{1}{2}$