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Kurt G1 partial Apartial y WeBWorK MATH WeBWorK MATH gPhys C fi k2/MATH 010A 030

ID: 1594434 • Letter: K

Question

Kurt G1 partial Apartial y WeBWorK MATH WeBWorK MATH gPhys C fi k2/MATH 010A 030 16W/2.6 DIRECTIONAL DERIVATIVES AND GRADIENT/6 0018 display Mod Math&sh; OldA 1&user; 0018 key nBf6Fdo2RmRIvwaJw3: SR O (AS Cn E Apps M ucR M Pcc If Facebook a My subscription WeBwork licethepie Time Warner Ca... fe Electronics, Car... other bookmarks com E LeBrown James D MA. Twitter Db Welcome, Kurt LancerPoint Log... Logged in as ktomo001. We BWork MATHEMATICAL ASSOCIATION 0F AMERICA WeBWork MATH 010A 030 16W 2.6 DIRECTIONAL DERIVATIVES AND GRADIENT 6 Courses 2.6 DIRECTIONAL DERIVATIVES AND GRADIENT: Problem 6 Previous Prob. List Next Homework Sets 2.6 DIRECTIONAL DERIVATIVES AND Problem 6 Password/Email Find the directional derivative off(x,y, 4xy at the point (-4,-1, 1) in the direction of the maximum rate of change off. fu (-4 Duf-4 Problems Problem 1 Problem 2 Preview Answers Submit answers Problem 3 Problem 4 You have attempted this problem 0 times Problem 5 You have 5 attempts remaining. Problem 6 Problem 7 WeBWorK 1996-2011 The WeBWork Project Display options View equations as: formattedText images Math Jax Show saved answers? 4:33 PM PSI Pr 2/14/2016

Explanation / Answer

The direction for the maximum rate of change is in the direction of the gradient f.

f = <4y, 4x, 2z>

So, the desired direction vector is
u = f(-4, -1, -1) / ||f(-4, -1, -1)|| = <-4, -16, -2>/269

Therefore,
D_u (-4, -1, -1) = f(4, -1, -1) · u
...................= <-4, -1, -1> · <-4, -1, -1>/269
...................= 269.