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Math Help - extreme values

  1. #1
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    Exclamation extreme values

    hi there

    in the shown example (attached ) picture i dont understand the circled phrases in red


    • what is fxy ? what did we derive to get 1
    • why is it local maximum??
    • what is the saddle point in this example

    i appreciate your help
    Attached Thumbnails Attached Thumbnails extreme values-extreme-values.jpg  
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  2. #2
    Super Member Matt Westwood's Avatar
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    f_{xy} is \frac {\partial^2 f}{\partial x \partial y}.

    That is, you differentiate f partially with respect to x, and then differentiate that partially with respect to y.

    When you plug x = -2, y = -2 into the given equation for f, you get 8.
    Last edited by mr fantastic; October 7th 2009 at 01:15 AM. Reason: Merged posts
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  3. #3
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    Quote Originally Posted by Matt Westwood View Post
    f_{xy} is \frac {\partial^2 f}{\partial x \partial y}.

    That is, you differentiate f partially with respect to x, and then differentiate that partially with respect to y.
    thank u i appreciate ur help but i still didnt get it how to derive with respect to (x and y) at the same time.
    i got all the other parts (with respect to x then with respect to y).
    if i consider both x and y constants i should get f(xy)= 4
    is it possible to show me how did we get (1) in that part
    thanks
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  4. #4
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by alex83 View Post
    thank u i appreciate ur help but i still didnt get it how to derive with respect to (x and y) at the same time.
    i got all the other parts (with respect to x then with respect to y).
    if i consider both x and y constants i should get f(xy)= 4
    is it possible to show me how did we get (1) in that part
    thanks
    You have your equation (which I can't see in front of me because you didn't type it in just copied the page in and I can't see it when I'm editing it).

    Partially differentiate it with respect to x (partially) to get the expression for f_x. That is, f_x = \frac {\partial f}{\partial x}. It's just a more compact notation for it.

    Then differentiate that partially with respect to y to get f_{xy}.

    That is, f_{xy} is (f_x)_y or \frac {\partial}{\partiial y} \left({\frac {\partial f}{\partial x}}\right).

    And when you work it out (they've done f_x for you) you get f_{xy} = 1.

    You'll probably find something about this in your text book.
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