feb28 - Math 10C Winter 2011 Prof Tesler Example from...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 10C, Winter 2011, Prof. Tesler Example from February 28, 2011 lecture Find the global minimum and global maximum of f ( x, y ) = x 2 - y 2 on the square - 1 x 1 , - 1 y 1 . The square is a closed region (it includes the perimeter); bounded (it’s finite); and the function f ( x, y ) is continuous on it. So by the Extreme Value Theorem, there is a global minimum and a global maximum of f ( x, y ) within the square. (As opposed to f ( x, y ) tending to ±∞ , or approaching a minimum/maximum without ever reaching it, etc.) We have three categories of candidate points to examine, and then we’ll compare them them to see which gives the global minimum and global maximum. Local minima and local maxima from the second derivatives test, provided that they are within the region (square). Points where f ( x, y ) is discontinuous within the region (square); (there aren’t any in this problem). Local minima and local maxima along the perimeter.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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