The surface of Lake Erehwon can be represented by a region D in the xy-plane such that the lake’s depth (in meters) at the point (x, y) is given by the expression 400 − 3x2 y2. If your calculus instructor is in the water at the point (1,−2), in which direction should she swim
(a) so that the depth increases most rapidly (i.e., so that she is most likely to drown)?
(b) so that the depth remains constant?
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