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

  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. Dick

    Dick 25,735
    Science Advisor
    Homework Helper

    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. 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. ... i can't figure out how to do the implicit differentiation on this. Could someone help me out with it?
     
  6. Dick

    Dick 25,735
    Science Advisor
    Homework Helper

    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. 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. Char. Limit

    Char. Limit 1,986
    Gold Member

    Why would you implicitly differentiate? Since 3 is an odd power, you can solve for y without losing any information...
     
  9. Dick

    Dick 25,735
    Science Advisor
    Homework Helper

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