Question

Materi Turunan
-Jawab dgn menggunakan cara-

Answer 1

Verified answer

Y = 5/(x^2 + 6) = 5(x^2 + 6)^-1
y' = -5(x^2 + 6)^-2 . 2x
y' = -10x/(x^2 + 6)^2

Kemiringan (gradien) : m = y'
m akan terkecil jika y'' = 0 (titik stasioner)

y' = -10x/(x^2 + 6)^2 = u/v
u = -10x => u' = -10
v = (x^2 + 6)^2 => v' = 2(x^2 + 6) . 2x = 4x(x^2 + 6)
y'' = (u' v - v' u)/v^2
=> (-10 (x^2 + 6)^2 - 4x(x^2 + 6)(-10x)) / ((x^2 + 6)^2)^2 = 0
=> (-10(x^2 + 6)^2 + 40x^2 (x^2 + 6)) / (x^2 + 6)^4 = 0
=> -10(x^2 + 6) [(x^2 + 6) - 4x^2] / (x^2 + 6)^4 = 0
=> -10(x^2 + 6) [6 - 3x^2] / (x^2 + 6)^4 = 0
=> -10 . -3 (x^2 - 2) / (x^2 + 6)^3 = 0
=> 30 (x + √2)(x - √2) / (x^2 + 6)^3 = 0
x = -√2 atau x = √2
m = y' = -10x/(x^2 + 6)^2
x = -√2 => m = 10√2 / (2 + 6)^2 = 5/32 √2
x = √2 => m = -10√2 / (2 + 6)^2 = -5/32 √2 ===> terkecil

y = 5/(x^2 + 6) => x = √2
y = 5/(2 + 6) = 5/8

Persamaan garis singgung (√2, 5/8) dan m = -5/32 √2
y - y1 = m(x - x1)
y - 5/8 = -5/32 √2 (x - √2) =====> kedua ruas dikali 32
32y - 20 = -5√2 (x - √2)
32y - 20 = -5√2 x + 10
32y + 5√2 x = 30