Let f(x, y) = 9 + x In(xy - 5). Study this function near the point (3, 2). a) The partial derivatives of f(x,y) are f,(x, y) = In(xy - 5) + ух and fy(x, y) = xy - 5 xy - 5 Both fy and f, are continuous functions for xy > 5 b) f(3, 2) = 6 and fy(3, 2) = 9 %3D c) Hence using Section 14.6 0 Theorem: 9 0 fis differentiable at (3, 2). d) Find the linearization L(x, y) of f(x, y) at (3,"2)." L(x, y) = 6x + 9y-27 e) The equation of the tangent plane at the point (3, 2, 9) to the surface z = f(x, y) is the equation
Let f(x, y) = 9 + x In(xy - 5). Study this function near the point (3, 2). a) The partial derivatives of f(x,y) are f,(x, y) = In(xy - 5) + ух and fy(x, y) = xy - 5 xy - 5 Both fy and f, are continuous functions for xy > 5 b) f(3, 2) = 6 and fy(3, 2) = 9 %3D c) Hence using Section 14.6 0 Theorem: 9 0 fis differentiable at (3, 2). d) Find the linearization L(x, y) of f(x, y) at (3,"2)." L(x, y) = 6x + 9y-27 e) The equation of the tangent plane at the point (3, 2, 9) to the surface z = f(x, y) is the equation
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Let
f(x, y) = 9 + x In(xy-5). Study this function near the point (3, 2).
a)
The partial derivatives of f(x,y) are
Fa(x, y) = In(xy- 5) + *
アー5
and f,(x, y) -
Both f, and f, are continuous functions for xy > 5
b)
fx(3, 2) = 6
and f(3, 2) = 9
%3D
%3D
c)
Hence using Section
14.6 0 ,
Theorem:90
Fis differentiable at (3, 2).
d)
Find the linearization L(x, Y) of f(x, y) at (3, 2)."
L(x, y) =
6x + 9y-27
%3D
e)
The equation of the tangent plane at the point (3, 2, 9) to the surface z = f(x, y) is the equation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc89a95b2-246d-47a4-b49c-326d31328d79%2Fad8dff82-352c-4c40-a8a6-d788bec8a233%2Fxq4ikd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let
f(x, y) = 9 + x In(xy-5). Study this function near the point (3, 2).
a)
The partial derivatives of f(x,y) are
Fa(x, y) = In(xy- 5) + *
アー5
and f,(x, y) -
Both f, and f, are continuous functions for xy > 5
b)
fx(3, 2) = 6
and f(3, 2) = 9
%3D
%3D
c)
Hence using Section
14.6 0 ,
Theorem:90
Fis differentiable at (3, 2).
d)
Find the linearization L(x, Y) of f(x, y) at (3, 2)."
L(x, y) =
6x + 9y-27
%3D
e)
The equation of the tangent plane at the point (3, 2, 9) to the surface z = f(x, y) is the equation
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