# Question:Making a procedure for saddlepoints

## Question:Making a procedure for saddlepoints

Maple
 > restart;
 > f:=(x,y)->x^4-3*x^2-2*y^3+3*y+0.5*x*y;
 (1)
 >

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

 > CriticalPoints:= [ solve( {diff(f(x,y),x)=0,diff(f(x,y),y)=0}, {x,y}) ];
 (2)
 >

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)

 > plot3d(f);
 >

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}) ?

 > ?student
 >

Some information to find in

 • 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
 2 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}) ];
 (3)
 >