Jawaban:

a) 24x - y + 8 = 0

b) • y = 4

• 9x -y - 32= 0

Penjelasan dengan langkah-langkah:

y = x (x-3)²

m = y' = 1. (x-3)² + x. 2(x-3)

m = (x-3)( x-3 +2x)

m =( x-3)(3 x-3 )

m = 3 (x-3)(x-1 )

a. absis : -1

x = -1

y = (-1) (-1-3)²

y = -16

m = 3 (x-3)(x-1 )

m = 3 (-1-3)(-1-1)

m = 24

Persamaan garis singgung

y - y1 = m ( x - x1)

y - (-16) = 24 ( x -(-1))

y + 16 = 24 x + 24

24x - y + 8 = 0

b.Ordinat 4

y = x (x-3)²

4 = x ( x²-6x+9)

x³-6x²+9x -4 = 0

(x-1)²(x-4) = 0

x = 1 → ( 1,4)

x = 4 → ( 4,4)

titik singgung ( 1,4)

m = 3 (x-3)(x-1 ) = 0

persamaan garis singgung

y - y1 = m ( x - x1)

y - 4 = 0

y = 4

titik singgung ( 4,4)

m = 3 (x-3)(x-1 ) = 3.1.3 =9

persamaan garis singgung

y - y1 = m ( x - x1)

y - 4 = 9 ( x - 4)

y -4 = 9x - 36

y = 9x - 36 +4

y = 9x - 32

9x -y - 32= 0