Matematika

Pertanyaan

1. persamaan garis singgung kurva y = -1/2x - 3// y = 1/3 + 2/3
2. persamaan garis singgung kurva y = x² - 2x + tegak lurus y = 1/2x + 1

1 Jawaban

  • 1. Soal  kurva = y = -1/2 x² - 3
    sejajar y  = 1/3 x + 2/3  --> m = -1/3

    m = y' = -x  --> x = - m = - (-1/3)
    x = 1/3  , y = 1/3 (1/3) + 2/3 = 7/9
    garis singgung --> y = 1/3(x - 1/3) + 7/9
    y = 1/3 x- 1/9 + 7/9 --> y = 1/3x +6/9
    y = 1/3 x + 3/2

    2. soal kurva = y = x² - 2x
    tegak lurus y = 1/2 x  + 1 -->m1 = 1/2
    m garis singgung = - 1/ m1 = - 2

    y'= m --> 2x -2 = -2
    2x = 0
    x = 0 , y = 1/2(0) + 1 --> y = 1
    garis singgung y = 2(x -0) + 1
    y = 2x + 1

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