Matematika

Pertanyaan

jika f(x) = 3x² - 5 per x - 6 maka f(0) - f'(0) =

2 Jawaban

  • f(x) = 3x^2 - 5 per x - 6
    f'(x) = 6x per 1 = 6x

    f(0) - f'(0)
    = {(3(0)^2 - 5 per 0 - 6) - (6 x 0)}
    = {(-5 per -6) - 0}
    = 5 per 6

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  • f(x) = (3x^2 - 5)/(x - 6)
    f(0) = (3.0^2 - 5)/(0 - 6) = -5/-6 = 5/6

    f(x) = (3x^2 - 5)/(x - 6) = u/v
    u = 3x^2 - 5 => u' = 6x
    v = x - 6 => v' = 1
    f'(x) = (u' v - v' u)/v^2
    f'(x) = (6x (x - 6) - 1 (3x^2 - 5)) / (x - 6)^2
    f'(0) = (6(0) (0 - 6) - 1(3(0)^2 - 5)) / (0 - 6)^2
    f'(0) = (0(-6) - 1(0 - 5)) / (-6)^2
    f'(0) = (0 - (-5)) / 36
    f'(0) = 5/36

    f(0) - f'(0) = 5/6 - 5/36 = (30 - 5)/36 = 25/36

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