Matematika

Pertanyaan

Harap bantuannya tentang bab persamaan garis singgung kurva
Harap bantuannya tentang bab persamaan garis singgung kurva

1 Jawaban

  • 4x - 24y - 1 = 0 => m = -a/b = -4/-24 = 1/6 karena tegak lurus
    m = -1/(1/6) = -6

    y = 2x^2 (x - 3) = 2x^3 - 6x^2
    y' = 6x^2 - 12x
    m = y'
    -6 = 6x^2 - 12x
    -6x^2 + 12x - 6 = 0
    x^2 - 2x + 1 = 0
    (x - 1)(x - 1) = 0
    x = 1
    y = 2x^2 (x - 3)
    x = 1 => y = 2(1)^2 (1 - 3) = 2 (-2) = -4

    Persamaan garis singgung di titik (1,-4) dan m = -6
    y - y1 = m(x - x1)
    y + 4 = -6(x - 1)
    y + 4 = -6x + 6
    y = -6x + 2

    6x + y = 2

    6x + y - 2 = 0