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Question: Making a procedure for saddlepoints

Question:Making a procedure for saddlepoints

janhardo 335 Maple
extrema plotting multivariate-calculus saddle-point
December 12 2021
0
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restart;
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f:=(x,y)->x^4-3*x^2-2*y^3+3*y+0.5*x*y;

proc (x, y) options operator, arrow; x^4-3*x^2-2*y^3+3*y+.5*y*x end proc

 (1)
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Critical points: tangentline in x direction and y direction are  0  for some points on the surface  f(x,y)  

 

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CriticalPoints:= [ solve( {diff(f(x,y),x)=0,diff(f(x,y),y)=0}, {x,y}) ];

[{x = 0.5935572277e-1, y = .7105957432}, {x = 1.191117672, y = .7741187286}, {x = 1.255942703, y = -.7776000848}, {x = -0.5877159444e-1, y = -.7036351094}, {x = -1.197482099, y = -.6326213916}, {x = -1.250162405, y = .6291421140}]

 (2)
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Seems that maple calculate 6 points on the surface with a default domain?

let me make a  3D plot of f  ( not specifying the domain values)

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plot3d(f);

 
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I calculated 6 critical points :how to show them in the plot? : i calculate the functionvalues for f
So now i do have x,y,z values for a 3D point
plot3D ({ f, points}) ?

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?student
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Some information to find in

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 Student[MultivariateCalculus]  ..link?
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Multivariate Calculus Study Guide

In order to make a procedure ( to make it general) out of the wanted calculated steps , i must first calculate these steps
List of wanted steps:

1. 

calculate (6 )critical points : i did

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investigate of the found critical points :are there saddle points among them?
Show this in a table

3. 

show a critical point with 2 section lines in this critical point intersected in a plot
4. 

show these critical points in a plot

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How to make table out of this list.CriticalPoints. for easy reading.?

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CriticalPoints:= [ solve( {diff(f(x,y),x)=0,diff(f(x,y),y)=0}, {x,y}) ];

[{x = 0.5935572277e-1, y = .7105957432}, {x = 1.191117672, y = .7741187286}, {x = 1.255942703, y = -.7776000848}, {x = -0.5877159444e-1, y = -.7036351094}, {x = -1.197482099, y = -.6326213916}, {x = -1.250162405, y = .6291421140}]

 (3)
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Download zadelpunten_procedure.mw
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