Loading ...
Sorry, an error occurred while loading the content.

local maximum, minimum, saddle point

Expand Messages
  • xhumga bernard
    freeware http://groups.yahoo.com/group/mathc/ * Calculus : local maximum, minimum, saddle point ************ Windows : Dev-C++ 4 Linux : gcc abc.c -lm Return
    Message 1 of 2 , Jul 8, 2006
    View Source
    • 0 Attachment
      freeware http://groups.yahoo.com/group/mathc/

      * Calculus : local maximum, minimum, saddle point

      ************

      Windows : Dev-C++ 4
      Linux : gcc abc.c -lm Return
      a.out Return

      ************

      * You can compile the *.c files directly without create a project.


      ************

      Let f be a function of two variables.
      A pair (a,b) is a critical point of f if either

      (I) f_x(a,b) = 0 and f_y(a,b) = 0
      (II) f_x(a,b) or f_y(a,b) does not exit.

      c16l_01a.c f : x,y,z -> -x**2 - 4*x - y**2 + 2*y - 1
      c16l_01b.c f : x,y,z -> x**2 + 4*y**2 - x + 2*y
      c16l_01c.c f : x,y,z -> x**3 + 3*x*y - y**3


      ************

      Let f be a function of two variables
      that has continuous second partial derivatives
      throughout an open disk R containing (a,b).

      If f_x(a,b) = f_y(a,b) = 0 and

      D(a,b) > 0,

      then f(a,b) is

      (I) a local maximum of f if f_xx(a,b) < 0
      (II) a local minimum of f if f_xx(a,b) > 0

      c16l_02a.c f : x,y,z -> -x**2 - 4*x - y**2 + 2*y - 1
      c16l_02b.c f : x,y,z -> x**2 + 4*y**2 - x + 2*y


      ************

      Let f be a function of two variables
      that has continuous second partial derivatives
      throughout an open disk R containing (a,b).

      If f_x(a,b) = f_y(a,b) = 0 and

      D(a,b) < 0,

      Then p(a,b,f(a,b)) is a saddle point on the graph of f.

      c16l_02c.c f : x,y,z -> x**3 + 3*x*y - y**3

      ************

      The members can try these links :

      http://groups.yahoo.com/group/mathc/files/C/D/c16l.zip
    • xhumga bernard
      17:49 08/07/06 freeware http://groups.yahoo.com/group/mathc/ * Calculus : local maximum, minimum, saddle point ************ Windows : Dev-C++ 4 Linux : gcc
      Message 2 of 2 , Jul 8, 2006
      View Source
      • 0 Attachment
        17:49 08/07/06
        freeware http://groups.yahoo.com/group/mathc/

        * Calculus : local maximum, minimum, saddle point

        ************

        Windows : Dev-C++ 4
        Linux : gcc abc.c -lm Return
        a.out Return

        ************

        * You can compile the *.c files directly without create a project.


        ************

        c16m_a1.c : Choose a critical point on the graph.
        c16m_a2.c : Verify if it is a local maximum.

        c16m_a3.c : Choose a critical point on the graph.
        c16m_a4.c : Verify if it is a local minimum.

        c16m_a5.c : Choose a critical point on the graph.
        c16m_a6.c : Verify if it is a saddle point.

        ************

        The members can try these links :

        http://groups.yahoo.com/group/mathc/files/C/D/c16m.zip
      Your message has been successfully submitted and would be delivered to recipients shortly.