Answer:
To identify the critical point, we set the derivative equal to zero, resulting in:
Calculating the second derivative yields:
This indicates that t = 3.4375 marks the minimum value for the function. Substituting this back into the original function gives us:
Thus, the minimum annual income is found at t = 3.43 (between the years 2008 and 2009), with a value of 25.094
Step-by-step explanation:
In this scenario, we have the function:
Where P represents the annual net income from 2007-2011, and
t is the number of years since early 2005
To discover the lowest income, we utilize the derivative given by:
Setting this derivative to zero allows us to find the critical point, leading to:
Calculating the second derivative reveals:
Therefore, we conclude that t = 3.4375 is the minimum value, substituting into the original function results in:
Thus, the minimum annual income occurs at t = 3.43 (between 2008 and 2009) with the value being 25.094