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
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Chapter1: Functions And Models
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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.
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,

Calculus homework question answer, step 1, image 1

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,

Calculus homework question answer, step 2, image 1

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)

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