(a) Show that u has a stationary point at (-2, 1), and determine the nature of this point. (b) The function u has a second stationary point. By considering simultaneously the conditions du/dx = du/dy = 0, show that this stationary point necessarily occurs when xy = -2. Hence use the condition du/dx = 0 to find the location of this second stationary point.
(a) Show that u has a stationary point at (-2, 1), and determine the nature of this point. (b) The function u has a second stationary point. By considering simultaneously the conditions du/dx = du/dy = 0, show that this stationary point necessarily occurs when xy = -2. Hence use the condition du/dx = 0 to find the location of this second stationary point.
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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can you please provide explanations
Transcribed Image Text:A5. The function u is defined by u(x, y) = x + 3xy² + x²y³.
(a) Show that u has a stationary point at (-2, 1), and determine the nature of this point.
(b) The function u has a second stationary point. By considering simultaneously the conditions
ди/дх du/dy = 0, show that this stationary point necessarily occurs when xy = -2.
Hence use the condition du/dx = 0 to find the location of this second stationary point.
=
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for the discrimanat here dont we do (Uxy)^2-(Uxx*Uyy)
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