Question

Determine an appropriate domain of the function. Identify the independent and dependent variables. A stone is thrown vertically upward from the ground at a speed of ​60 m/s at time t= 0. Its distance d​ (in m) above the ground​ (neglecting air​ resistance) is approximated by the function ​f(t)= 60t- 5t^2.

An appropriate domain is:_______

Answer 1

the domain of the function = [0,12]

Explanation:

Given that:

f(t) = 60 t - 5t²

at time t = 0

f(0) = 60 (0) - 5(0)²

f(0) = 0

the differential of f(t) is:

f(t)' = 60 - 10t

for the maximum height

f'(t) = 0

i,e

60 - 10t = 0

60 = 10t

t = 60/10

t = 6

Now, t = 6,

f(6) = 60(6) - 5(6)²

f(6) = 360 - 180

f(6) = 180

Hence, after 6 seconds, the stone is noticed to have raise to 180 m and 180 m drop after 6 seconds.

Hence, the domain of the function = [0,12]