Lupe Garcia is the efficiency expert for a large manufacturing company. She finds that the average worker who arrives on the job when the morning shift begins at 8:00 A.M. will have assembled f(x) = −x³ + 6x² + 15x units x hours later.

a. Lupe wants to find the rate at which the average worker is assembling units x hours after the morning shift begins. What is this rate?

b. At what rate is the average worker assembling units at 9:00 A.M.? How many units does the average worker actually assemble between 9:00 A.M. and 10:00 A.M.?

c. Lupe expects the assembly rate to be less at noon when the morning shift ends than at 9:00 A.M. Is this true?