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3. Find the value of the directional derivative at the particular point Po for the given function in the direction of U. (a) g(x, y) = y² tan² x; U = -}V3 î+ } ĵ; Po(}r, 2) (b) f(x, y) = xe²»; U = } î + }V3 î; Po(2,0)

3. Find the value of the directional derivative at the particular point Po for the given function in the direction of U. (a) g(x, y) = y² tan² x; U = -}V3 î+ } ĵ; Po(}r, 2) (b) f(x, y) = xe²»; U = } î + }V3 î; Po(2,0)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.3: Vectors
Problem 60E
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Definition 3.32 If f is a function of two variables x and y such that f. and fy exist, then the gradient of f, denoted by Vƒ (read as “del f"), is given by V{(r,y) = f.(z. y) i + f,(r, y) j. Note that the gradient Vf(x, y) is a vector and Df(1,9) = U - V j(z, y). Suppose a is the radian measure of the angle between U and Vf. Then D7f(z, y) = U·Vf(r, y) = ||U|||Vf(r, y)|| o a. (3.2) Equation (3.2) tells us that D#f(x, y) will be a maximum when cos a = 1; so that we have ||Vf(x, y)|| gives the maximum value of D7f at the point (r, y).
Transcribed Image Text:Definition 3.32 If f is a function of two variables x and y such that f. and fy exist, then the gradient of f, denoted by Vƒ (read as “del f"), is given by V{(r,y) = f.(z. y) i + f,(r, y) j. Note that the gradient Vf(x, y) is a vector and Df(1,9) = U - V j(z, y). Suppose a is the radian measure of the angle between U and Vf. Then D7f(z, y) = U·Vf(r, y) = ||U|||Vf(r, y)|| o a. (3.2) Equation (3.2) tells us that D#f(x, y) will be a maximum when cos a = 1; so that we have ||Vf(x, y)|| gives the maximum value of D7f at the point (r, y).
3. Find the value of the directional derivative at the particular point Po for the given function in the direction of U. (a) g(x, y) = y² tan² x; U = -}V3 î+ } ĵ; Po(}r, 2) (b) f(x, y) = xe²»; U = } î + }V3 î; Po(2,0)
Transcribed Image Text:3. Find the value of the directional derivative at the particular point Po for the given function in the direction of U. (a) g(x, y) = y² tan² x; U = -}V3 î+ } ĵ; Po(}r, 2) (b) f(x, y) = xe²»; U = } î + }V3 î; Po(2,0)
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