Consider the function f .x; y; z/ D x2y C yz C z2. (a) Find
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Consider the function f .x; y; z/ D x2y C yz C z2. (a) Find the directional derivative of f at .1; ?1; 1/ in the directi
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Consider the function f .x; y; z/ D x2y C yz C z2. (a) Find the directional derivative of f at .1; ?1; 1/ in the direction of the vector i C k. (b) An ant is crawling on the plane x C y C z D 1 through .1; ?1; 1/. Suppose it crawls so as to keep f constant. In what direction is it going as it passes through .1; ?1; 1/? (c) Another ant crawls on the plane x C y C z D 1, moving in the direction of the greatest rate of increase of f: Find its direction as it goes through .1; ?1; 1/.
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