The annual net income of a company for the period 2007–2011 could be approximated by P(t) = 1.6t2 − 11t + 44 billion dollars (2 ≤ t ≤ 6), where t is the time in years since the start of 2005.

According to the model, during what year in this period was the company's net income the lowest?

And we can set equal this derivate to 0 in order to find the critical point and we got:

And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094

Step-by-step explanation:

For this case we have the following function:

Where P represent the annual net income for the period 2007-2011 and

And t represent the time in years since the start of 2005

In order to find the lowet income we need to use the derivate, given by:

And we can set equal this derivate to 0 in order to find the critical point and we got:

And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094