An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 08:00AM will have assembled f(x) = x3 + 6x2 + 15x transistor radios x hours later.

a. Derive a formula for the rate at which the worker will be assembling radios after x hours.

b. At what rate will the worker be assembling radios at 09:00AM?

c. How many radios will the worker actually assemble between 09:00AM and 10:00AM?