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Math Help - Multivariable Caculus Leverl Curves

  1. #1
    Member zangestu888's Avatar
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    Multivariable Caculus Leverl Curves

    Am studying for my final exam lol, this question is confusing me as well,

    the equation give is f(x,y)=x^2/4 + y^2/9

    (a) Sketch at least three labeled level curves of f and the gradient vector at a point on each of them.

    Kay I know how to draw the level curves i set f(x,y)=z say , z constant i get an ellipse but how do I draw the gradient vectos at each point? as they say from reading from my textbook it says its orthogonal to the level curves so i just draw perpendicular lines to the points on the level curves.

    (b) Find an equation to the tangent plane, at f(2,3) thats just using the the partial dervitives of fx and fy i think
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For your gradient vectors --yes they are orthognal to the curves but
    in the direction of increasing z --so on one level curve the gradient is in the direction of a level curve of greater z value

    For your second question yes

    z = fx(2,3)*(x-2) +fy(2,3)*(y-3) + f(2,3)
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  3. #3
    Member zangestu888's Avatar
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    What do you mean exactly by the same level as increasing z value I quite get what you say! thank!
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  4. #4
    MHF Contributor Calculus26's Avatar
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    if you have a level curve where say z = 1 and one where z = 2 then the gradient on the level curve z= 1 is orthogonal and points toward the level curve where z = 2
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  5. #5
    Member zangestu888's Avatar
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    Kay gotcha am gonna work on that graph now thanks! dude!
    Last edited by mr fantastic; April 21st 2009 at 08:12 PM. Reason: Added a w
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