What does f_xy mean?

Assume we have a function f(x,y) of two variables like f(x,y) = x2 y. The partial derivative fx is the rate of change of the function f in the x direction. We also can see that xx means: it is positive if the surface is bent concave up in the x direction and negative if it is bent concave down in the x direction. What it the interpretation of the derivative fxy? One can interpret it as the rate of change of the slope in the x-direction as one moves into the y direction.

Can we read of the value of f_xy from a level curves? For one of the following contour maps, the derivative f_xy is nonzero at the center of the picture. For which one? Solution

Questions and comments to knill@math.harvard.edu

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