Aplikasi Turunan

y = cos 2x

(i)

gradien m = y' = -2 sin 2x

x = π/6

m = -2 sin (2 × π/6)

m = -2 sin (180°/3)

m = - 2 sin 60°

m = -2 × 1/2 √3

m = - √3

(ii)

titik singgung

x = π/6 = 180°/6 = 30°

y = cos 2x

y = cos (2 × 30°)

y = 1/2

pgs dg m = - √3 di titik singgung (π/6,1/2) :

y = m(x - x1) + y1

y = - √3 (x - π/6) + 1/2

y = - √3 x + 1/6 √3 π + 1/2

(iii)

gradien garis normal = m2

m2 = -1/m1

m2 = -1/(-√3)

m2 = 1/3 √3

pers garis normal m = 1/3 √3 di titik (π/6,1/2) :

y = 1/3 √3 (x - π/6) + 1/2

y = 1/3 √3 x - 1/18 √3 π + 1/2

garis normal ⊥ garis singgung kurva