55. Temperature on a circle Let T = f(x, y) be the temperature at the point (x, y) on the circle x = cos t, y = sin t, 0 < t < 27 and suppose that Әт 8х — 4y, дх Әт 8y – 4x. ду a. Find where the maximum and minimum temperatures on the circle occur by examining the derivatives dT/ dt and d²T/dt². b. Suppose that T = 4x² – 4xy + 4y². Find the maximum and minimum values of T on the circle.
55. Temperature on a circle Let T = f(x, y) be the temperature at the point (x, y) on the circle x = cos t, y = sin t, 0 < t < 27 and suppose that Әт 8х — 4y, дх Әт 8y – 4x. ду a. Find where the maximum and minimum temperatures on the circle occur by examining the derivatives dT/ dt and d²T/dt². b. Suppose that T = 4x² – 4xy + 4y². Find the maximum and minimum values of T on the circle.
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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Transcribed Image Text:55. Temperature on a circle Let T = f(x, y) be the temperature at
the point (x, y) on the circle x = cos t, y = sin t, 0 < t < 27 and
suppose that
Әт
8х — 4y,
дх
Әт
8y – 4x.
ду
a. Find where the maximum and minimum temperatures on the
circle occur by examining the derivatives dT/ dt and d²T/dt².
b. Suppose that T = 4x² – 4xy + 4y². Find the maximum and
minimum values of T on the circle.
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