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Math Help - implicit differentiation (horizontal tangent line)

  1. #1
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    implicit differentiation (horizontal tangent line)

    Given the curve x^2+xy+y^2=9

    a) Find y'

    x^2+xy+y^2=9

    Taking the derivative of the above equation and using product rule for xy, i get,
    2x+(y+xyy')+2yy' = 0
    xy'+2yy' = -2x-y
    y'(x-2y)=-2x-y

    Answer:
    y' = (-2x-y)/(x+2y)

    b) Find all points on the curve at which the tangent line is horizontal


    Is a) correct? and also how do i do letter b)? i have no clue what to do. thanks!
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  2. #2
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    To find the points that are horizontally tangent find y' of 0.


    0=(-2x-y)/(x+2y)

    Because the slope will be zero when it is horizontally tangent.

    Hope it helps.
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  3. #3
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    oh okay, but im still totally lost, what do i do after that?
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  4. #4
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    Solve you x and y and plug them into point slope form.
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