Web Works #7 Spring 2009

# D find the maximum rate of change of f at p 61 pt

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Unformatted text preview: v. D v 1v f Note: Your answer should be a number. D. Find the maximum rate of change of f at P. 6.(1 pt) Given that that near (1,1,1) the curve of intersection of the surfaces Note: Your answer should be a number. E. Find the (unit) direction vector u in which the maximum rate of change occurs at P. i j u Note: Your answers should be numbers. 4.(1 pt) Consider the surface deﬁne u x y and v x y in terms of x and y near the point xy 1 1 and u v 11. Compute the partial derivatives ∂u ∂u 11 11 ∂x ∂y ∂v ∂v 11 11 ∂x ∂y Note that all answers are numbers. ¥ 5.(1 pt) Given that the surface x7 y3 y9 z3 z5 x6 2xyz 5 has the equation z f x y in a neighbourhod of the point 1 1 1 with f x y differentiable, ﬁnd the derivatives ∂f 11 ∂x ∂f 11 ∂y ∂2 f 11 ∂x2 and the equation of the tangent plane at 1 1 1 z1 x1 y1 £ ¢¡ 3z 5 zx ¢  ¢  ¡ £ ¡¢ £ ¢ £ ¡ ¦¥¥ £ £¢ ¡ £¢ ¡ £ ¢ ¡ ¢¡¡ ¥¢ ¦ yz £ ¢¡ 0 and xy ¢¡¡ ¥ 3xyz ¢¦ ¥ ¦ ¥ ¥ 0 5yv2 ¡ £ ¥ ¢ ¡ ¢ ¡ £ ¢¡ £ ¢ ¡ £ ¢ ¡ £ ¢ ¡ ¥ £ ¢¡ £ £ ¢ ¦ £ ¢ ¡ ¥¢ ¦ ¥¢ ¦ ¥ ¥  £ £ £ ¢ ¦ ¢ £ ¢ ¡ ¢ ¡ £ ¢¡ £ ¢ ¡ ¥ ¦ ¥ 1 5 ¥ £ £ ¤¢ ¡ ¡  £ ¥ ¥   £ Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR yv xu £ ¥ ¥ 50 £  £ ©¢ ¡ ¡ 4xu2 ¥ ¢¡¡ ¢¡¡ ¦ £ ¥ £ ¢ £ ¢ ¥ ¥ has the parametric equations x f t y g t z t with f g differentiable, the derivatives f 1 g 1 are f1 g1 and the tangent line to the curve of intersection at (1,1,1) is x1 s, y 1 s, z 1 s 7.(1 pt) The equations ¡ ¥ 9z2 ¥ 25y2 z6 ¥ 16x2 y3 £ x7 6...
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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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