Extreme values

Exercise

1.: Find the extreme value of the following functions．
(a): $\displaystyle{f(x,y) = 2x^2 + y^2 -xy - 7y}$
(b): $\displaystyle{f(x,y) = \frac{x}{y^2} + xy }$
(c): $\displaystyle{f(x,y) = x^3 + y^3 - 3xy}$
(d): $\displaystyle{f(x,y) = (x^2 + y^2)^2 - 2(x^2 - y^2)}$
2.: Find the Taylor expansion of the following function around with the nd degree in .
(a): $\displaystyle{f(x,y) = e^x \cos{y}, \ (a,b) = (0,0)}$
(b): $\displaystyle{f(x,y) = \log{(x + y^2)}, \ (a,b) = (2,1)}$