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AS_98244341-Visitor
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March 18, 2021
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Problem with finding stationary points of a partial derivative function and guess values

  • March 18, 2021
  • 1 reply
  • 11393 views

Hi all,

I hope all of you are enjoying life!

I am working on finding the stationary points of function of several variables f(x,y). 

Problems:

1- How do I solve a system of equations without knowing its guess values? I took me a while to get the values x=5 and y=10 otherwise the equation solver does not work. 

2- It seems that I have inputted the equations wrong to find the nature of stationary points ? Can anyone give me advice or tell me why is this not working? So, I1 should be a negative number(I think)

The correct answer is: a saddle point at (1,-1) [according to the maths textbook] 

 

(Update: problem 3: how do solve an equation that has more than one solution? when I used solve block it only returns one solution)

Please have a look at my worksheet.

Best answer by Werner_E

Primes infamous auto-labelling feature often is more a PITA than helpful.

You have to manually label the variables after "solve" to be "Variable" and NOT "(-)" (automatic).

Werner_E_0-1616184314820.png

 

And in case you are not interested in the non-real solutions, you may add an appropriate assume modifier:

Werner_E_1-1616184398731.png

Werner_E_0-1616184822016.png

If you make f an additional argument of "HesseDet", you may use this very same function for any of your given functions without having to redefine any more.

 

 

1 reply

ttokoro
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
March 19, 2021

image.png

ttokoro_0-1616118144741.png

 

image.pngimage.pngimage.pngimage.png

t.t.
    A
    AS_98244341-VisitorAuthor
    1-Visitor
    March 19, 2021

    Hi,

    Thanks for the reply!

    Why does it not work when I use the formula shown in the maths textbook? So, saddle point should give an answer less than zero in that equation in the screenshot.

    ttokoro
    21-Topaz I
    ttokoro21-Topaz I
    21-Topaz I
    March 19, 2021

    The saddle point  is [x,y,z]=[1,-1,-1]   Another point is [0,0,0], which is left above, is not saddle point, 

    image.png

    t.t.
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