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Homework Help: Implicit Differentiation; Tangent Line

  1. Jul 21, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the equation of a tangent line at the curve at point (-3√3, 1)

    x^(1/3) + y^(1/3) = 4


    2. Relevant equations
    Point-slope:
    y-1=m(x-1)

    3. The attempt at a solution

    I took the derivative of that equation and resulted in
    -y^(2/3)/x^(2/3)

    When I tried plugging in x and y to get slope, the equation got very messy and I couldn't get a number out of it. Can anyone help me out?
     
    Last edited: Jul 21, 2010
  2. jcsd
  3. Jul 21, 2010 #2

    Mark44

    Staff: Mentor

    Looks like there is a typo here.
    This would be the line with slope m, that passes through (1, 1).
    It's hard to tell whether this is correct, since the original equation likely has a typo. If you typed '=' in place of '+', then you have a sign error in your derivative. Also, it would be helpful to have an equation for your derivative; e.g., y' = y^(2/3)/x^(2/3).
     
  4. Jul 21, 2010 #3
    Here's all of my work:

    (1/3)x^(-2/3) + 1/3y^(-2/3)(dy/dx) = 0

    (dy/dx)1/3y^(2/3) = -1/3x^(2/3)
    dy/dx = -3y^(2/3)/3x^(2/3)
    dy/dx = -y^(2/3)/x^(2/3)

    I hope that helps find my problem. This is where I tried plugging in the x value and everything got complicated.

    1/(-3√3)^(2/3)
     
  5. Jul 21, 2010 #4

    Mark44

    Staff: Mentor

    What is the original equation? I can't tell if your work is correct without knowing the original equation.
     
  6. Jul 21, 2010 #5

    Mark44

    Staff: Mentor

    (-3√3)^(2/3) can also be written as ((-3√3)^2)^(1/3)
     
  7. Jul 21, 2010 #6
    x^(1/3) + y^(1/3) = 4

    This is the original equation. Sorry about the typo before.
     
  8. Jul 21, 2010 #7

    Mark44

    Staff: Mentor

    That's what I thought, but I wanted to make sure. You should have enough information to complete the problem now.
     
  9. Jul 21, 2010 #8
    Just to make sure, the slope is 1/3?
     
  10. Jul 21, 2010 #9

    Mark44

    Staff: Mentor

    I get -1/3.
     
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