Web Works #7 Spring 2009

# 21 pt the

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Unformatted text preview: PM. ¥ ¥ ¢¡ ¥ £ ¤¢ ¡ ¥ £ ¨¢ ¡ £ ¥ ¢ §¡ ¦ £ ¥ £ ©¢ ¦ ¥¢ ¦ 2.(1 pt) The function f x y z x4 y3 y2 z2 z5 x2 4x 4y 3z increases most rapidly at the point P 1 1 1 in the direction i j k. The rate of increase at P in this direction is . The rate of increase at P in the direction of the point Q 3 2 6 is . The equation of the tangent plane to the level surface f x y z 14 is x1 y1 z1 0. x 3.(1 pt) Suppose f x y 4 4 and v 2i j. ,P y A. Find the gradient of f . ∇f i j Note: Your answers should be expressions of x and y; e.g. “3x 4y”. B. Find the gradient of f at the point P. ∇f P i j Note: Your answers should be numbers. C. Find the directional derivative of f at P in the direction of the displacement vector...
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## This note was uploaded on 11/09/2011 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.

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