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Specific slope for directional derivative?

  1. Jun 11, 2008 #1
    Is there a direction where the rate of change is 18, at the point (-1,2) on the function f(x,y) = (x^2)(y^3)+xy?

    So I found the gradient of this function, picked a random direction vector u = ( a / (a^2+b^2)^(1/2) , b / (a^2+b^2)^(1/2) ) and took the dot product, and set it to 18... however, I have one equation with two unknowns and no idea how to proceed.

    Thank you.
  2. jcsd
  3. Jun 11, 2008 #2
    don't do that mess..

    just say u = <a,b> is unit vector
    so, a^2+b^2 = 1 would be your second equation
    <a,b>.del f = 18 your first equation

    I found del f to be <-14,11>
    this might be wrong, because I didn't recheck my work
  4. Jun 11, 2008 #3


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    Homework Helper

    It doesn't matter if you have 2 unknowns. You're interested in the direction, not the magnitude of the direction vector. Express either a or b in terms of the other and then normalise the vector (a,b)
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