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Math Help - implicit functions

  1. #1
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    implicit functions

    ok so I've got the implicit differentiation down, now i need help on how to find the tangent line...for example...

    x^2 + y^2 - 5x + 7y = 13

    dy/dx = (-2x+5)/(2y+7)

    now it asks...

    Under what condition on x is the tangent line to the curve horizontal?

    Under what condition on y is the tangent line to the curve vertical?

    can i get some help on how to go about this...thanks

    mathaction
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  2. #2
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    1)If the tangent line is horizontal then it has no slope or a slope of 0. So in order to find out where the slope is zero, in this case, set -2x+5=0

    2)If the tangent line is verical then we have divided by zero because there is an infinite slope. In this case, we need the denomiator to equal zero so find out what value of y makes it so.
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  3. #3
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    Quote Originally Posted by Jameson View Post
    1)If the tangent line is horizontal then it has no slope or a slope of 0. So in order to find out where the slope is zero, in this case, set -2x+5=0

    2)If the tangent line is verical then we have divided by zero because there is an infinite slope. In this case, we need the denomiator to equal zero so find out what value of y makes it so.
    yeah i figured this one out already...i took a second look, then felt stupid, but thanks anyway...
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