Math

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Use implicit differentiation to find the slope of the tangent line to the curve y/( x + 4 y) = x^4 – 4
at the point (1,-3/13)

  • Math -

    y/(x+4y) = x^4 – 4
    (y'(x+4y) - y(1+4y'))/(x+4y)^2 = 4x^3
    (x+4y-4y)y' = 4x^3 (x+4y)^2 +y
    y' = 4x^2 (x+4y)^2 + y/x

    y'(1) = 4(1)(1-12/13) + (-3/13)/1 = 1/13

  • Math -

    Steve,
    That still isn't the correct answer :(

  • Math -

    Hmmm. Have you any clues? what is the correct answer? see any mistakes in my agebra?

    If you go to wolframalpha.com and type in

    derivative y/(x+4y) = x^4 – 4

    you will see the value of y', which is what I got above. So, if my answer is wrong, I must have erred in my evaluation at (1, -3/13).

  • Math -

    Ah. I see I didn't take (1-12/13)^2
    You can fix that.

  • Math -

    I first changed the equation to:

    y = x^5 - 4x + 4x^4y - 16y
    now differentiate ....

    y' = 5x^4 - 4 + (4x^4)y' + 16x^3 y' - 16y'

    y'( 1 - 4x^4 + 16) = 5x^4 - 4 + 16x^3
    using the point (1, 3/13)
    y' (1-4-16) = 5 - 4 - 48/13
    -19y' = -35/13
    y' = 35/247

  • Math -

    oops: 16x^3 y' ?

  • Math -

    yup, that's the one
    should have been 16x^3y
    should have realized there were too many y' hanging around
    Thanks

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