Question: An efficiency study conducted for the Undercover Farms Cooperative showed that the number of cases of cucumbers packed by the average worker x hours after starting work at 8 a.m. is given by the function

for \(0\le x\le 4\)

The cooperative wishes to validate this function in terms of the time of the work day for which the efficiency of the staff is increasing as well as the time of the work day for which the efficiency of the staff is decreasing.

As a young graduate on staff, you are asked to undertake the validation. Discuss and demonstrate how you would use Differentiation to find

(a) The times of the work day (i.e. values of x) for which the efficiency of the staff is increasing;

(b) The times of the work day (i.e. values of x) for which the efficiency of the staff is decreasing.