Matematika

Pertanyaan

F'(x) = x - √x dan f(4) = -3

1 Jawaban

  • f'(x) = x - √x = x - x^1/2
    f(x) = integral (x - x^1/2) dx
    f(x) = 1/2 x^2 - 2/3 x^3/2 + C
    f(x) = 1/2 x^2 - 2/3 x√x + C
    f(4) = 1/2 . 4^2 - 2/3 . 4√4 + C = -3
    => 8 - 16/3 + C = -3
    => C = -11 + 16/3 = -17/3
    Jadi
    f(x) = 1/2 x^2 - 2/3 x√x - 17/3

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