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Implicit Differentiation Problem (stuck at a point)

  1. Feb 17, 2004 #1

    Cod

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    Here is the problem:

    Find the equation of the line which is tangent to the curve at the point (1,3): 8x^3y^2 + x^2y^5 + 6 = 4y^4 - 3x^4


    Here is what I've done so far (I'm stuck now):

    (24x^2)(y^2) + (8x^3)(2y dy/dx) + (2x)(y^5) + (x^2)(5y^4 dy/dx) = (16y^3 dy/dx) + 12x^3


    Where do I go from here? Collect like terms? Any help is greatly appreciated.
     
  2. jcsd
  3. Feb 17, 2004 #2

    Doc Al

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    Staff: Mentor

    Start plugging in numbers and solve for dy/dx.
     
  4. Feb 17, 2004 #3

    Cod

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    Re: Re: Implicit Differentiation Problem (stuck at a point)

    So I just plug in a 1 where x's are and a 3 where the y's are?
     
    Last edited: Feb 17, 2004
  5. Feb 17, 2004 #4

    Doc Al

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    Re: Re: Re: Implicit Differentiation Problem (stuck at a point)

    You got it.
     
  6. Feb 17, 2004 #5

    Cod

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    But the differentiation process isn't done. I haven't even factored out the dy/dx yet to get the derivative. I thought I plugged in the points AFTER I found the derivative...?
     
  7. Feb 17, 2004 #6

    Doc Al

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    Sure it is. All you need is dy/dx at one point, not at all points.
    No need to do that!
    That would be the hard way. Don't do it.

    I think you are confusing what you need to do here, which is find the slope at a particular point, with a much harder problem: finding dy/dx as a function of x for all x. Lot's of luck with that one.
     
  8. Feb 17, 2004 #7
    Unless I am mistaken, shouldn't the last term be -12x^3 ?
    You have a + there.

    I figured dy/dx=-34.
    That would make the equation of the tangent line y=-34x+37.

    Can someone confirm this? I am rusty...

    Whoops, caught an error myself...edited to add the +37 in my answer!!!
     
    Last edited: Feb 17, 2004
  9. Feb 17, 2004 #8

    Doc Al

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    Good catch.
    No. The line had better contain the point (1,3).
     
  10. Feb 17, 2004 #9
    Yeah, I have to think a little longer next time.

    y=-34x+37.
     
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