The City Council proposed to utilize government-owned land with an area of 12,150 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an...

The City Council proposed to utilize government-owned land with an area of 12,150 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following:


a. the rate at which the total average number of COVID cases is increasing at x=10 tents and dx/dt=1 tent per day, given that if 30 tents are built, the average number of COVID cases per tent will be 7 cases while the average number of cases will increase by 2 per tent for each additional tent on the same area due to overcrowding.



Please give me a step-by-step process or a detailed solution in solving the given problem. Also kindly explain the conclusion on why it is the correct answer.




Most importantly, verify that the value/s is/are extremum/extrema using either first/second derivative test.