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4.9 Conditional extrema

1.

(a) $\displaystyle{f(1,0) = f(-1,0) = 1 {\rm minimum}, f(0,1) = f(0,-1) = 3 {\rm maximum}}$

=2.6zw =1(b) $\displaystyle{f(2,0) = 0 {\rm minimum}, f(-2,0) = 8 {\rm maximum}}$

(c) $\displaystyle{f(0,-1) = -1 {\rm minimum}, f(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}) = \frac{1}{2} + \sqrt{2} {\rm maximum}}$

2.

$\displaystyle{\frac{1}{4}}$