Definition 3.32 If ƒ is a function of two variables r and y such that f. and fy exist, then the gradient of f, denoted by Vƒ (read as “del f"), is given by V/(1,v) = f.(x, y) î + f,(x, y) j. Note that the gradient Vf(x,y) is a vector and Dyf(r,y) = U - V f(r,y). Suppose a is the radian measure of the angle between U and Vf. Then D7f(r, y) = U -Vf(x, 9) = ||U|||V/(r,y)|| 0o a. (3.2) Equation (3.2) tells us that Df(x, y) will be a maximum when cos a = 1; so that we have ||V f(x, y)| gives the maximum value of D7f at the point (x, 9).
Definition 3.32 If ƒ is a function of two variables r and y such that f. and fy exist, then the gradient of f, denoted by Vƒ (read as “del f"), is given by V/(1,v) = f.(x, y) î + f,(x, y) j. Note that the gradient Vf(x,y) is a vector and Dyf(r,y) = U - V f(r,y). Suppose a is the radian measure of the angle between U and Vf. Then D7f(r, y) = U -Vf(x, 9) = ||U|||V/(r,y)|| 0o a. (3.2) Equation (3.2) tells us that Df(x, y) will be a maximum when cos a = 1; so that we have ||V f(x, y)| gives the maximum value of D7f at the point (x, 9).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 45E
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