aplikasi turunan

y = x^n → y' = n x^(n - 1)

jarak, f(t) = at³ + bt² - 5t

kecepatan, v (t) = f'(t) = 3at² + 2bt - 5

v(1) = 0

3a.1² + 2b.1 - 5 = 0

3a + 2b = 5 ... (1)

v(5) = 0

3a.5² + 2b.5 - 5 = 0 bagi (5)

15a + 2b - 1 = 0

15a + 2b = 1 ... (2)

3a + 2b = 5

15a + 2b = 1

kurangkan

-12a = 4

a = -4/12

a = -1/3

3a + 2b = 5

3(-1/3) + 2b = 5

-1 + 2b = 5

2b = 5 + 1

b = 3

v(t) = 3at² + 2bt - 5

v(t) = 3(-1/3)t² + 6t - 5

v(t) = -t² + 6t - 5

percepatan, a(t) = v'(t)

a(t) = -2t + 6

saat t = b = 3

a(3) = -2.3 + 6

a(3) = 0

percepatan saat t = 3 adalah 0 m/s².