Use the data in the table to approximate f'(9), the instantaneous rate of change in the amount of dirt removed, in cubic meters per hour, at time t=9 hours.

Question

Information given:

ƒ(t) = { 48t + t² - (t³⁄12) for 0≤ t ≤ 6 g(t) for 6≤ t ≤12

Table :

t (hours) 6 8 10 12

g(t) (cubic meters) 306 376 428 474

Answer 1

We can either assume g(t) is a cubic - like f(x) - or demonstrate it.

Determine the differences of g(t)

306 376 428 474

70 52 46

18 6

12

a = 12 / 3!

a = 2

g(t) = 2t³ + bt² + c^t + d

Use any three of the four pairs to develop a system of three equations and solve for b, c, and d.