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Lagrange multipliers: Extreme values of a function subject to a constraint

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Uploaded by on Nov 17, 2008

I discuss and solve an example where the points on an ellipse are sought that maximize and minimize the function $f(x,y) := xy$. The method of solution involves an application of Lagrange multipliers. Such an example is seen in 1st and 2nd year university mathematics.

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Uploader Comments (DrChrisTisdell)

  • The hum in the background sounds like a UFO is ready to land.

  • @swampwiz Haha! Actually, it is the noise from the air-con units for the building that lie directly outside the window.

  • Perfect!!! Thanks a lot

  • Great!! Thanks!

  • Is that how you pronounce Lagrange at 0:57 ? I said it that way and my tutor gave me the dirty haha :)

  • Hahaha!!! So much for my Aussie-French accent??!! :-)

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  • Wow Dr. Tisdell you are a remarkable prof! Even though I just came here for review after having learnt this already, I can tell all viewers that this is a spot on example/explanation of Lagrange multipliers! I wish you were a professor at Concordia University in Montreal, I would love to have you as a prof one day!

  • Perfectly explained! I came here clueless after 2 hours in the textbook and left 7 minutes and 31 seconds later with full understanding

  • oh yeah !!! thank u

    DrChrisTisdell it's very clear!

  • Hi Yoyaya. If you listen carefully, at 6.42 I discuss how to show which points lead to maxima and which points lead to minima.

    In particular, if you evaluate $f$ at the first two points then you get $1/(2\sqrt{2})$. At the other two points $f$ has value $-1/(2\sqrt{2})$. It is easy to see that the maximum of these set of values is $1/(2\sqrt{2})$ and the minimum value is $-1/(2\sqrt{2})$. Thus, the 2nd-derivative test is not required.

    Hope I am being clear here and thanks for watching!

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