Matematika

Pertanyaan

Bantuin dong tolong nomor 16-18 aja.makasih
Bantuin dong tolong nomor 16-18 aja.makasih

1 Jawaban

  • 16) f(x) = 2x^3 - 3x^2 + 4x
    f'(x) = 6x^2 - 6x + 4
    f'(2) = 6(2)^2 - 6(2) + 4 = 24 - 12 + 4 = 16

    17) f(x) = (x - 2)^2/(x√x)
    = (x^2 - 4x + 4) / (x . x^1/2)
    = (x^2 - 4x + 4)/x^3/2
    = (x^2 - 4x + 4).x^-3/2
    = x^1/2 - 4x^-1/2 + 4x^-3/2
    f'(x) = 1/2 x^(-1/2) + 2x^(-3/2) - 6x^(-5/2)
    = 1/(2x^1/2) + 2/(x^3/2) - 6/(x^5/2)
    = 1/(2√x) + 2/(x√x) - 6/(x^2 .√x)
    f'(4) = 1/(2√4) + 2/(4√4) - 6/(4^2 √4)
    = 1/4 + 2/8 - 6/32
    = 1/4 + 1/4 - 3/16
    = (4 + 4 - 3)/16
    = 5/16

    18) f(x) = (x^2 + 1/x)^2
    = x^4 + 2x + 1/x^2
    = x^4 + 2x + x^-2
    f'(x) = 4x^3 + 2 - 2x^-3
    = 4x^3 + 2 - 2/x^3
    f'(2) = 4(2)^3 + 2 - 2/2^3
    = 32 + 2 - 1/4
    = 32 + 1 + 1 - 1/4
    = 33 + 3/4
    = 33 3/4