Question

Diketahui kurva x³ + y³ - 9xy = 0
Carilah persamaan garis singgungnya di titik (2,4)

Tips : materi turunan

Answer 1

Mgs nya dicari dengan turunan implisit

d( x³ + y³ - 9xy) = d(0)

  3x²+3y².y' - 9d(xy) = 0 <= untuk turunan xy pakai aturan turunan perkalian 2 fungsi ( d(u.v) = d(u).v + d(v).u )

  3x²+3y².y' - 9(1.y+1.y'.x) = 0

  x²+y².y' - 3(y+xy') = 0

 x² +y²y' - 3y - 3xy' = 0

y'(y²-3x) = 3y - x²

y' = (3y-x²)/(y²-3x)

mgs = (3.4-2²)/(4²-3.2)

mgs = (8)/(10)

mgs = 4/5

persamaan garis singgungnya :

y - 4 = (4/5)(x-2)

y = 4/5 x - 8/5 + 4

5y = 4x - 8 + 20

5y = 4x + 12

5y-4x = 12