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Math Help - Curve

  1. #1
    Member Rimas's Avatar
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    Curve

    Given the curve x^2-xy+y^2=9
    (A) write a general expression for the slope of the curve.
    (B) Find the coordinates of the points on the curve where the tangents are vertical.
    (C) At the point (0,3) find the rate of change in the slope of the curve with respect to x.
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    Chaneysville, PA
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    Can you do implicit differentiation?.

    2x-xy'-y+2yy'=0

    Solve for y'.

    For the vertical tangents:

    Eliminate all terms without y' and we're left with:

    -xy'+2yy'=0

    y'(-x+2y)=0

    -x+2y=0

    y=\frac{x}{2}

    Sub this back into your original and solve for x to find the points where there are vertical tangents.

    The reason this works has to do with the limit as y'\to {\infty}
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  3. #3
    Junior Member Godfather's Avatar
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    for c the slope = -.5 but what does respect to x mean
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