Solution:
The correct answer is ts the forth one which is the contour plot of f(x,y) = x y.
The one above is f(x,y) = x^{2}+y^{2} which has f_{xy}=0 at the center.
The first one is just f(x,y)=g(x)
for some function of x, like x^{2}, there is no y dependence so that f_{xy}=0
there too. In the third case, f_{x} is constant zero on the y axes as these are maxima.

Math21b | Math 21a | Fall 2008 |
Department of Mathematics |
Faculty of Art and Sciences |
Harvard University