calculus

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there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve

  • calculus -

    The point (0,1) lies in the "interior" of the parabola
    y = 3x^2.
    There is no tangent to the curve that will pass through (0,1).

    check your typing.

  • calculus -

    there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,-1 find the x coordinates of the point where the tangents line intersect the curve, please show working.

  • calculus -

    ahhh, now it makes sense.

    let the point of contact be (a,b)

    slope of tangent by the grade 9 way = (b+1)/a
    slope of tangent by Calculus is
    dy/dx = 6x
    so at the point (a,b), slope = 6a

    then 6a = (b+1)/a
    6a^2 = b+1
    but since (a,b) lies on the curve, b = 3a^2
    so
    6a^2 = 3a^2 + 1
    a^2 = 1/3
    a = ± 1/√3

    so the x coordinates of the two tangents are 1/√3 and -1/√3

  • calculus -

    find the equation of the tangent line of the curve y=root x divideed by x+1 at the point p = 2, root 2 divided by 3. show working please.

  • calculus -

    find the equation of the tangent line to the curve y = 2√2/x+1 at the point p=1,2/3.please show working. i would appreciate if you do it before 12:05pm today

  • calculus -

    use implcit differenciation to find an eqaution of both the tangent line to the ellipse:
    2x^2 + 4y^2 = 36
    that passes through the points: 14,3

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