Lagrange Multipliers

  • Thread starter Cherizzle
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  • #1
Cherizzle
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Hi There I would like help on a question about Lagrange multipliers.

Question: Consider the intersection of two surfaces: an elliptic paraboloid z=x^2 + 2*x + 4*y^2 and a right circular cylinder x^2 + y^2 = 1. Use Lagrange multipliers to find the highest and lowest points on the curve of the intersection.

What I have so far:
I managed to find my critical points using lagrange multipliers. But now I don't know how to describe whether my points are at maximum or minimum...
The points I found were: (2/3, -[tex]\sqrt{5}[/tex]/3) and (-[tex]\sqrt{2}[/tex]/6, 1)
 

Answers and Replies

  • #2
uart
Science Advisor
2,797
21
Hi Cherizzle. Are you sure that's supposed to be z=x^2 + 2*x + 4*y^2 and not z=x^2 + 2*x*y + 4*y^2
 

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