b) f(x, y) = ln(x² + y²) at the point (1, -2) and the direction in which it occurs.Maximum rate of change:Direction (unit vector) in which it occurs: a) f(x, y, z) = x + y/z at the point (-1, 2, 5) and the direction in which it occurs.Maximum rate of change:Direction (unit vector) in which it occurs:>

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Answered: b) f(x, y) = ln(x² + y²) at the point…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 58E

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Find the directions of maximum and minimum change of f at the given point, and the values of the maximum and minimum rates of change. f{x, y) = 4y²e*, (2, –4) The maximum change is 32e V37 ; in the direction (-192e“, 32e®); The minimum change is –32e V37 ; in the direction (192e", -32e). The maximum change is 32e6 The minimum change is –32e 6 V37 :; in the direction (192e, -32e ). V37 ; in the direction (-192e6, 32e ); The maximum change is 32e V37 ; in the direction (192e, -32e); The minimum change is –32e V37 ; in the direction (-192e", 32e). The maximum change is 32e V37 ; in the direction (192e ,–32e ); The minimum change is –32e 6 V37 :; in the direction (-192e, 32e ).
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b) f(x, y) = ln(x² + y²) at the point (1, -2) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs: