Web Works #7 Spring 2009

Web Works #7 Spring 2009 - Assignment 7 MATH262 Winter 2009...

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Hector Hernandez Assignment 7 MATH262, Winter 2009 due 4/8/09 at 11:59 PM. 1. (1 pt) The function f x y x 4 y 4 4 xy 3 x 2 y 4 increases most rapidly at the point P 1 1 in the direction i j . The rate of increase at P in this direction is . The rate of increase at P in the direction of the point Q 2 1 is . The equation of the tangent line to the level curve f x y 15 at the point P is x 1 y 1 0. 2. (1 pt) The function f x y z x 4 y 3 y 2 z 2 z 5 x 2 4 x 4 y 3 z increases most rapidly at the point P 1 1 1 in the di- rection 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 x 1 y 1 z 1 0. 3. (1 pt) Suppose f x y x y , P 4 4 and v 2 i j . A. Find the gradient of f . f i j Note: Your answers should be expressions of x and y ; e.g. “3 x 4 y ”. B. Find the gradient of f at the point P . f P i j Note: Your answers should be numbers.
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