# WW7 - Jignesh Patel due 11/07/2010 at 11:59pm EST. ....

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Jignesh Patel Assignment 7 MATH262, Fall 2010 due 11/07/2010 at 11:59pm EST. . 1. (1 pt) The function f ( x , y ) = x 4 + y 2 + 3 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 ( 3 , 6 ) is . The equation of the tangent line to the level curve f ( x , y ) = 14 at the point P is ( x - 1 )+ ( y - 1 ) = 0. 2. (1 pt) The function f ( x , y , z ) = x 4 y 4 + y 5 z 3 + z 3 x 5 + 5 x + 2 y + 5 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 ( 4 , 6 , 5 ) is . The equation of the tangent plane to the level surface f ( x , y , z ) = 15 is ( x - 1 )+ ( y - 1 )+ ( z - 1 ) = 0. 3. (1 pt) Suppose f ( x , y ) = x y , P = ( - 1 , - 1 ) and v = i + 4 j . A. Find the gradient of

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## This note was uploaded on 12/21/2010 for the course MATH 262 taught by Professor Faber during the Spring '08 term at McGill.

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WW7 - Jignesh Patel due 11/07/2010 at 11:59pm EST. ....

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