{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assignment 5 - = x 2 y 2-1 2 y a Use the method of Lagrange...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 237 Assignment 5 Due: Friday, Oct 31st 1. Find and classify the critical points of the following functions and determine the shape of the level curves near each critical point. a) f ( x, y ) = 1 2 x 2 + 3 y 3 + 9 y 2 - 3 xy + 9 y - 9 x . b) g ( x, y ) = x 3 + y 3 - 6 y 2 - 3 x + 9. c) h ( x, y ) = ( x + y )( xy + 1). 2. Find the maximum and minimum of f ( x, y ) = x 3 - 3 x + y 2 + 2 y on the region bounded by the lines x = 0, y = 0, x + y = 1. 3. Find the maximum and minimum of f ( x, y ) = x 2 - y 2 on the region x 2 + y 2 1. 4. Find the points on the surface z = x 2 + y 2 that is closest to the point (1 , 1 , 0). 5. Let
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) = x 2 + y 2-1 2 y . a) Use the method of Lagrange multipliers to find the maximum and minimum points of f ( x,y ) on the curve y = √ 1-2 x 2 . b) Let R be the region bounded by the curve y = √ 1-2 x 2 and the x-axis. Find the maximum and minimum value of f ( x,y ) on the region R . 6. Find the maximum and minimum values of f ( x,y ) = y on the piriform curve defined by y 2 + x 4-x 3 = 0....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern