Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Multivariable calculus yummy in my tummy

  1. Sep 18, 2007 #1
    [Question]
    Hi, my teacher gave us this problem, and he couldn't figure out why
    method was incorrect and why I got the answer I did.

    Given we know the gradient slope = <-56,1.886> at the point (2,0) on a
    surface f(x,y), in what direction, expressed as a unit vector, is f
    increasing most rapidly?





    [Difficulty]
    I solved the problem like this:

    Max slope = magnitude of gradient slope
    (gradient slope) dot (unit vector) = 56.03
    -56.03Ux + 1.866Uy = 56.03
    sqt(Ux^2 + Uy^2) = 1

    Solving the system Ux= -.9977 Uy=.0672

    The only problem is, by definition, I should be able to get the unit
    vector by taking the gradient slope vector and dividing by the
    magnitude of the gradient vector. or,

    <-56/56.03, 1.886/56.03> = <Ux,Uy> = <-.9994,.0336>

    The weird thing is, the correct Uy value is almost exactly half of
    mine...what's going on???

    [Thoughts]

    I tried a similiar technique for finding where the ∇f = 0

    <-56, 1.866> dot (unit vector) = 0

    -56.03Ux + 1.886Uy = 0
    sqt(Ux^2 + Uy^2) = 1

    Solving the system this time I got the correct answer, why here and
    not there?
     
  2. jcsd
  3. Sep 19, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I understand that the 56.03 is the magnitude of the given vector but the coefficient of Ux should be -56, not -56.03.

     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Multivariable calculus yummy in my tummy
  1. Multivariable Calculus (Replies: 2)

  2. Multivariable Calculus (Replies: 3)

Loading...