Is there an easy way to show that if f(x,y) is twice-differentiable on [0,1]x[0,1] with continuous second-order partial derivatives, then there must exist a point at which (d/dx)(d/dy) f(x,y) equals f(0,0)-f(0,1)-f(1,0)+f(1,1)? (I wonder if forums like math-fun, and sci.math in its heyday, are bad for a mathematician's brain. The above problem is probably a fairly standard exercise in advanced calculus, and in the old days, I would've had to wait until coffee hour to ask a colleague, by which time my own subconscious would have dredged up the needed facts and supplied the answer. Nowadays, I can just post the question and wait for someone in the 24-hour-a-day virtual coffee hour to post an answer. So my brain doesn't get as much exercise. Then again, my subconscious has more chew-toys to play with, thanks to *other* people's questions!) Jim Propp