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Find an equation of the tangent line to the graph of the function f

  1. Sep 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point.
    (x - y - 1)3 = x; (1, -1)



    3. The attempt at a solution
    x3-y3=1
    3y2(dy/dx)-3x2=0
    3y2(dy/dx)=3x22
    (dy/dx)=3y2/3x2
    (dy/dx)=x2/y2
    slope = (dy/dx) = 1

    y-(-1)= 1(x-1)
    y=x-2

    thats wrong -.-
    i tried making it dy/dx = x/y and still wrong.
    where am i messing up? I'm pretty sure it has to do with the x at the end but i have no idea what to do with it!
    We just learned derivatives so I'm still messing up with them.
     
  2. jcsd
  3. Sep 29, 2010 #2

    Dick

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    What has x^3-y^3=1 got to do with the problem? Your equation is (x-y-1)^3=x. Find y' using implicit differentiation.
     
  4. Sep 29, 2010 #3
    Yea, i thought i was deriving it wrong :) Ok, let me go back and look at my notes to see how to do implicit differentiation.
    Thanks
     
  5. Sep 29, 2010 #4
    ... i can't figure out how to do the implicit differentiation on this. Could someone help me out with it?
     
  6. Sep 29, 2010 #5

    Dick

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    The derivative of u^3 is 3*u^2*u'. Put u=x-y-1. What do you get? Is that the part that's confusing you?
     
  7. Sep 29, 2010 #6
    I'm getting confused on the dx/dy part. I'm not even sure i understand how to do this right.
    I thought i had to have them all cubed then get the derivative of x3-y3-13 but obviously that's not right since your first response was what did x3-y3= 1 have to do anything.

    So is it 3x2*u and 3y2*u -1? and then i add the dx/dy part somewhere? Or am i just way off here :(
    Sorry, we just learned this stuff today and it still hasn't really sunk in.
     
  8. Sep 29, 2010 #7

    Char. Limit

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    Why would you implicitly differentiate? Since 3 is an odd power, you can solve for y without losing any information...
     
  9. Sep 29, 2010 #8

    Dick

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    Good point. If you aren't comfortable with implicit differentiation, try it that way. They both work.
     
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