It is a known fact that after birth, an infant normally loses weight and then starts growing. Let us suppose that based on data collected at maternity hospitals, the average weight W (in lbs.) of infants over the first 14 days (two weeks) following birth is given by the functional relationship
where time t is measured in days. Note that t can take any value between 0 and 14. Now, when will a newborn baby start to grow? Obviously, the baby will start to grow after its weight has reached the minimum value. So, we need to determine the day (i.e., the value of t) on which W will be the minimum.
First, try to solve this problem using a trial and error approach.
Then, solve the problem analytically by using some systematic methods.