Right, this is annoying me

Announcements
    • Thread Starter
    Offline

    3
    ReputationRep:
    Apologies it's not in latex. Working out stationary points of:

    z=4xy - x^4 - y^4

    dz/dx = 4y-4x^3 = 0

    dz/dy = 4x-4y^3 = 0

    I solve dz/dx and get x = y^1/3. I substitute this into dz/dy and get y = 0, y = 1. I'm missing a result.The stationary points should be (0,0), (-1,-1), ), (1,1)Where does the (-1,-1) come from?!

    I'm being really stupid..
    Offline

    3
    ReputationRep:
    (Original post by hezzlington)
    Apologies it's not in latex. Working out stationary points of:

    z=4xy - x^4 - y^4

    dz/dx = 4y-4x^3 = 0

    dz/dy = 4x-4y^3 = 0

    I solve dz/dx and get x = y^1/3. I substitute this into dz/dy and get y = 0, y = 1. I'm missing a result.The stationary points should be (0,0), (-1,-1), ), (1,1)Where does the (-1,-1) come from?!

    I'm being really stupid..
    Initially I assumed you would have accidentally lost a solution by having incorrectly divided through by a variable somewhere in your simplification, but doing so would ommit the (0,0) solution and not the (-1,-1) solution so I'm not quite sure what you've done?

    In any case from dz/dx = 4y-4x^3 = 0 we get x=y^1/3 or x^3=y which then when subbed into dz/dy = 0 gives x=x^9 (or y=y^9).

    y=y^9 is satisfied by y=0,-1,1 which correspondingly gives solutions (x,y) = (0,0), (-1,-1) and (1,1) so I'm not sure about your issue?

    A mistake might have been to write y=y^9 => 1=y^8 => y=+-1 which loses the (0,0) solution because you have artificially lowered the order of the equation but since you are missing (-1,-1) I'm not sure whats gone wrong without seeing your workings...

    Hope this helps.

    Edit: Unless you've just made the elementary oversight of forgetting -1^(2n-1) = -1 for all positive integers n.
    Offline

    3
    ReputationRep:
    (Original post by In One Ear)
    A mistake might have been to write y=y^9 => 1=y^8 => y=+-1 which loses the (0,0) solution because you have artificially lowered the order of the equation but since you are missing (-1,-1) I'm not sure whats gone wrong without seeing your workings...
    I'm pretty sure the OP got to the point y^{1/3} = y^3 and then simply failed to realise (-1,-1) was a solution; looks fairly clear they were just spotting roots by inspection and it seems fairly easy to fail to recognize that y being -ve is an option here even though we're taking the cube root.

    (Original post by hezzlington)
    ..
    Without wanting to "nag", I'll point out that even if you didn't find (-1, -1) yourself, you really should have been able to verify that (-1, -1) was a solution to your equation. Since verification is usually easier than finding solutions, it's a good habit to get into, both with your own solutions (to make sure you've not made a silly mistake), and also solutions provided to you. (For a provided solution, you are not so much checking the solution is correct, but that your equations do actually "work" for the solution).
 
 
 
Write a reply… Reply
Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: October 6, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Poll
Which is the best season?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.