Suppose f is a smooth function of x and y, and at the point (1,1), [itex]\partial[/itex]f/[itex]\partial[/itex]x = 1, [itex]\partial[/itex]f/[itex]\partial[/itex]y = -1.
Find the unit vector u such that Duf(1,1) = 0
Duf(1,1) = [itex]\nabla[/itex]f(1,1) * u = 0
The Attempt at a Solution
My answer was merely u= k, which is the unit vector k of course (I don't know how to put the symbol on this. Work it out, I don't see how it is wrong. I will tell you why they said that I was wrong, and I will give my argument after an answer or two.