3 Directional derivatives Question 1: What are the directional derivatives of the following functions along the given directions u, at the given points P? • f(x,y)=√ along the direction u = (1,-1) at the point (1, 2)? f(x, y, z)= In(x+y) along the direction u = (2,0, 1) at the point (1, 1, 1)? Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, 7/4), What unit direction leads to the steepest ascent? What unit direction leads to the steepest descent? • What unit directions should one travel to stay level? Plot the function using Wolfram Alpha using an appropriate viewing window centered around the point P. Mark the directions of steepest ascent, descent and level sets, and compare them against your results.

3 Directional derivatives Question 1: What are the directional derivatives of the following functions along the given directions u, at the given points P? • f(x,y)=√ along the direction u = (1,-1) at the point (1, 2)? f(x, y, z)= In(x+y) along the direction u = (2,0, 1) at the point (1, 1, 1)? Question 2: Given the function f(x, y) = sin(x + y), at the point P(π/3, 7/4), What unit direction leads to the steepest ascent? What unit direction leads to the steepest descent? • What unit directions should one travel to stay level? Plot the function using Wolfram Alpha using an appropriate viewing window centered around the point P. Mark the directions of steepest ascent, descent and level sets, and compare them against your results.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.5: Systems Of Linear Equations In More Than Two Variables

Problem 30E

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