Matematika

Pertanyaan

tolong dijawab kk beserta caranya
tolong dijawab kk beserta caranya

1 Jawaban

  • f(x) = 2(x)^(-1) mk f'(x) = - 2(x)^(-2) = - 2/x²
    Krn f'(x) selalu bernilai negatif, mk gradien grs singgung selalu negatif
    a) x=2 mk y=2/2=1
    m1 = f'(1)= 2/1² = 2
    Grs singgung : y-y1=m1(x-x1)
    y-1 = 2(x-2)
    y=2x-3
    Grs normal : m2= - (1/m1) = - ½
    y-y1 = m2(x-x1)
    y-1 = - ½(x-2)
    y = - ½x + 2

    b) y = - 1 mk - 1 = 2/x atau x = - 2
    m1=f'(-2)=2/(-2)²=½
    Grs singgung : y-y1=m(x-x1)
    y+1=½(x+2)
    y=½x
    Grs normal : m2= -1/m1 = -1/(½) = - 2
    y-y1=m2(x-x1)
    y+1= - 2(x+2)
    y = -2x-5