Question

A drug is injected into the bloodstream of a patient at time t = 0. The concentration of the drug in the bloodstream t hours later is approximated by:
C(t) =
.28t t2 + 4
, 0 ≤ t ≤ 24
When is the concentration increasing? When is it decreasing? When does it achieve its maximum?

Answer 1

There is a typo in the equation: 
The equation need to be f(t)= 28t-t2+4
You need to calculate the derivative of f(t): f'(t)= 28-2t
f is increasing if f'(t) is positive ==> 28-2t>0 ==> t<14
f is decreasing if f'(t) is negative ==> 28-2t<0 ==> t>14
f reach its maximum  when f'=0 ==> 28-2t=0 ==> t=14

The concentration is increasing between for 0 < t < 14
The concentration is decreasing between for 14 < t < 24
The maximum is achieved when t=14

I hope this will help