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Slope of tangent

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    show that the tangent line to the curve y=x^3 at any point (a,a^3) meets the curve again at a point where the slope is four times the slop at (a,a^3).


    2. Relevant equations
    y=3x^2, point slope formula


    3. The attempt at a solution
    Not really sure where to begin. A hint should be enough.
     
  2. jcsd
  3. Dec 7, 2011 #2

    micromass

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    Can you find the equation of the tangent line at a?
     
  4. Dec 7, 2011 #3
    That would be, y=3a^2?
     
  5. Dec 7, 2011 #4

    micromass

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    No, where in earth did you get that?? A tangent line is a line. Its equation must contain an x and a y variable.
     
  6. Dec 7, 2011 #5
    Not sure what you are asking for. Could you clarify?
     
  7. Dec 7, 2011 #6

    micromass

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    I'm asking for the equation of the tangent line at the curve. How do you find the tangent line at a curve?? What is the slope of such a tangent line??
     
  8. Dec 7, 2011 #7

    HallsofIvy

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    Do you know what the equation of a line, perhaps with slope m and passing through point [itex](x_0, y_0)[/itex] looks like?
     
  9. Dec 7, 2011 #8
    I got y=3a^2*x -2a^3 for the tangent line. Is that alright?
     
  10. Dec 7, 2011 #9
    The equation of a line is y = m x + b. You need to find the right slope m and intercept b that will make the line be the right one that is tangent and touches a certain point.
     
  11. Dec 7, 2011 #10
    Yes, I do have an idea how it may look like. A straight line touching the curve and then intersecting the function at some other point where the slope is four times the value of the tangent line.
     
  12. Dec 7, 2011 #11

    HallsofIvy

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    The scary thing is that you think that answers my question. I asked about what the equation looks like and you said nothing about an equation.
     
  13. Dec 7, 2011 #12
    Well, that means that I misunderstood your question. I think this thread has had a bad start. Thank you.
     
  14. Dec 7, 2011 #13

    eumyang

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    This is correct. Now find out where else does this line intersect with y = x3. Set the two right hand sides equal to each other and solve for x (treating a as a constant).
     
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