Results are out! Find what you need...fast. Get quick advice or join the chat
Hey there Sign in to join this conversationNew here? Join for free

Lagrange multipliers question help please :)

Announcements Posted on
Got a question about Student Finance? Ask the experts this week on TSR! 14-09-2014
    • Thread Starter
    • 2 followers
    Offline

    ReputationRep:
    Find the rectangle in the ellipse  x^2 + 4y^2 = 1 with the smallest perimeter.

    I know that if  L = f(x,y) + \lambda g(x,y) then  \lambda g(x.y) = \lambda(x^2 + 4y^2 - 1) .

    However in the solutions it says that  f(x,y) = 4x + 4y . Why isnt this  2x+2y for the perimeter of the rectangle? Or is this a mistake in the solution? :/

    Thanks
    • 0 followers
    Offline

    ReputationRep:
    4x+4y is the perimeter of the rectangle.

    Think for a moment, the ellipse is one which is clearly centered at the origin.

    Hence, the length and breath of the rectangle would have to span both the -ve/+ve x and y axes in a symmetrical fashion to sit snugly within the ellipse.

    The horizontal side of the rectangle would be 2x.

    The vertical side of the rectangle would be 2y.

    Hence, perimeter would be 2* (2x+2y)= 4x+4y

    Hope this helps. Peace.

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. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: May 23, 2012
New on TSR

Writing your personal statement

Our free PS builder tool makes it easy

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