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March 26, 2017

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Use implicit differentiation to find the slope of the tangent line to the curve at the point (4,1)

-1x^2 - 4xy + 3y^3 = -29

I differentiated both sides and solved for dy/dx and got 2x-4y/9y^2-4x. Then I plugged in X and Y and got -4/7

but when i enter my answer it's wrong. What is the right answer? Where did I go wrong?

  • calculus; implicit differentiation - ,

    I got (2x+4y)/(9y^2-4x) for dy/dx

    I bet your error was in the derivative of
    -4xy
    which is -4x(dy/dx) - 4y

    check your signs.

  • calculus; implicit differentiation - ,

    Thanks a lot, it was the signs that was wrong.

  • calculus; implicit differentiation - ,

    Differentiate both sides of the equation with respect to x, with y being a function of x.

    -2x -4y -4x*dy/dx +9y^2*dy/dx = 0
    dy/dx = [2x +4y]/[9y^2 -4x]
    When x=4 and y = 1, I get
    dy/dx = (8 + 4) /(9 - 16) = -12/7

  • calculus; implicit differentiation - ,

    Thanks :)

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