You are walking on the graph of f(x,y)= ycos(pi(x)) - xcos(pi(y)) + 10 , standin

Question

You are walking on the graph of f(x,y)= ycos(pi(x)) - xcos(pi(y)) + 10 , standing at the point (2,1,13). Find an x,y direction you should walk in to stay at the same level. Show all work. Write out/explain all steps.

Explanation / Answer

First we calculate ?f = < ?f/?x, ?f/?y > ?f = < -py sin(px)-cos(py), cos(px)+px sin(py) > At x = 2, y = 1 ?f(2,1) = < -p sin(2p)-cos(p), cos(2p)+2p sin(p) > ?f(2,1) = < 0-(-1), 1+0 > ?f(2,1) = < 1, 1 > Now we need to walk in direction of vector u, so that ?f(2,1)·u = 0 One such directions is < 1, -1 >, another is < -1, 1 > General solution: t < 1, -1 >, for any scalar t

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