## local maximum, minimum, saddle point

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• 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
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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
• 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
• 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
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