6.7 2変数関数の極値

1.

(a) $(1,4)$で極小値 -14(b) 極値なし (c) $(1,1)$で極小値$-1$(d) $(\pm 1,0)$で極小値$-1$

2.

(a) $${f(x,y) = 1 + x + \frac{1}{2}(x^2 - y^2)}$$

(b) $${\log{3} + \frac{1}{3}(x-2) + \frac{2}{3}(y-1) - \frac{1}{18}(x-2)^2 - \frac{2}{9}(x-2)(y-1) + \frac{2}{9}(y-1)^2 + \cdots }$$