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Help with basic Calculus (Equation of a Tangent Line) Please?

  1. Dec 1, 2013 #1
    This is my first post, and I'm excited to be able to receive quality help from what seems to be a good place. I'll attempt to start using the proper format and make it easy for everyone to read, thank you for the help! This should be a simple problem, but I seem to have forgotten how to do it.


    1. The problem statement, all variables and given/known data
    Write the equation of the line tangent to the curve 3x3+y3=10xy at the point (1,3)


    2. Relevant equations
    3x3+y3=10xy


    3. The attempt at a solution
    my attempt revolved around getting x and y on separate sides of the equation, then taking the derivative of each side. I ended up getting:

    y'(x)=(10y-9x2)/(-10x+3y2)

    For some reason I thought to plug set that equal to 0 and then plug in my x and y coordinates and then plug that value into x for my original equation, but I know something went completely wrong somewhere, so I'm wondering at what point I went wrong and was wondering if there were a few starting steps I could get to do a problem like this. Thanks!
     
  2. jcsd
  3. Dec 1, 2013 #2

    Dick

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    The tangent to the curve at (1,3) is given by y'(1). That doesn't have to be zero. Find what it is by putting x=1 and y=3 into the derivative formula you so correctly derived.
     
  4. Dec 1, 2013 #3
    Hi Spencer! Welcome to PF! This is a great resource, and not only for HW help.

    Your equation for the derivative is correct. I'm not sure what you're setting equal to 0; at this point plug in your values for x and y to get the value for the derivative, or equivalently the slope. What would you do next, now that you have a point and a slope?
     
  5. Dec 1, 2013 #4
    Thank you so much for your replies!!!

    I believe that the number I get after plugging in would then be slope (m) and then I could easily plug that into y=mx+b and get my full answer. Such a simple problem that I over-thought!
     
  6. Dec 1, 2013 #5
    Almost. That should be the final form of the equation after simplifying. The equation you plug the numbers into is slightly different: ##y - y_1 = m (x - x_1)##
     
  7. Dec 1, 2013 #6
    Ohh, thank you. Is it also possible to find b first using y=mx+b and then to plug b back into the slope intercept form, or is that considered incorrect procedure?
     
  8. Dec 1, 2013 #7

    Dick

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    That is a fine procedure.
     
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