4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this ellipse, find: 1. the ones with the largest and smallest values of y. 2. the ones with the largest and smallest values of x.
4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this ellipse, find: 1. the ones with the largest and smallest values of y. 2. the ones with the largest and smallest values of x.
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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Question
Transcribed Image Text:4) Consider the ellipse x? – xy + y? = 3. From all points (x, y) of this
ellipse, find:
1. the ones with the largest and smallest values of y.
2. the ones with the largest and smallest values of x.
Expert Solution
Step 1
1. Note that the smallest and largest value of y occur when dy/dx =0.
Taking derivative on both sides,
Largest value of y is at (1,2) and smallest value is at (-1,-2)
Step 2
1. Note that the smallest and largest value of x occur when dx/dy =0.
Taking derivative on both sides,
Now, solving for y for x = 2 and -2 gives y = x/2, so y = 1 and -1.
Largest value of x is at (2,1) and smallest value is at (-2,-1)
Step by step
Solved in 3 steps with 3 images
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