Answered: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u…

Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum and minimum directional derivative at P and give a vector along which this value is attained.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 30E

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Question

Let f(x,y,z) = x² y−xy²+z³, P(1,1,2), u is the vector from P to
Q(1, −2, −2). Determine the maximum and minimum directional derivative at P and give a vector along which this value is attained.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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