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Math Help - Implicit Differentitationl;finding equation

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    Implicit Differentitationl;finding equation

    Find all the points of the elispe 3x^2+2y^2=12 where the tangent line has slope 1. Make a sketch of the elispe and the tangent line to confirm your answer as well.
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    Hello,

    Quote Originally Posted by lemontea View Post
    Find all the points of the elispe 3x^2+2y^2=12 where the tangent line has slope 1. Make a sketch of the elispe and the tangent line to confirm your answer as well.
    Differentiate :

    6x+2(y^2)'=0

    Using the product rule :
    (y \cdot y)'=y'y+yy'=2yy'.

    Substituting :

    6x+4yy'=0

    We want y'=1

    --> 6x+4y=0 \implies y=-\frac{3x}{2}


    Substituting in the equation of the ellipse :

    3x^2+2\left(-\frac{3x}2\right)^2=12

    3x^2+\frac{9x^2}{2}=12

    x^2+\frac{3x^2}{2}=4

    \frac{2x^2+3x^2}{2}=4

    5x^2=8

    \implies x=\pm \dots
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