Problem 3. The surface of a dome to be installed on the roof a house can be modelled through the function of two variables f (x,y)=4-x² - y². With respect to the height of the dome, only consider the positive part of the function to be above the house, i.e., (f (x, y) 20). a. Find the domain of the function considering the previously mentioned constraint. b. Graph in the xy plane the level curves corresponding to c= {0, 1, 2, 3, 4 }. c. Find all first and second order partial derivatives. d. Find the coordinate (xy) of the highest point of the dome. Prove why this is in fact the maximum point. e. Find the range of the function, considering the initial constraint (f (x,y)20).
Problem 3. The surface of a dome to be installed on the roof a house can be modelled through the function of two variables f (x,y)=4-x² - y². With respect to the height of the dome, only consider the positive part of the function to be above the house, i.e., (f (x, y) 20). a. Find the domain of the function considering the previously mentioned constraint. b. Graph in the xy plane the level curves corresponding to c= {0, 1, 2, 3, 4 }. c. Find all first and second order partial derivatives. d. Find the coordinate (xy) of the highest point of the dome. Prove why this is in fact the maximum point. e. Find the range of the function, considering the initial constraint (f (x,y)20).
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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answer d and e please :)
Transcribed Image Text:Problem 3. The surface of a dome to be installed on the roof a house can be modelled through the function of two variables
f (x, y)= 4-x² -y². With respect to the height of the dome, only consider the positive part of the function to be above
the house, i.e., (f (x,y)20).
a. Find the domain of the function considering the previously mentioned constraint.
b. Graph in the xy plane the level curves corresponding to c = { 0, 1, 2, 3, 4 }.
c. Find all first and second order partial derivatives.
d. Find the coordinate (xy) of the highest point of the dome. Prove why this is in fact the maximum point.
e. Find the range of the function, considering the initial constraint (f (x, y) 20).
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