***** PARTS A AND B ALREADY CORRECT, FIND PART C *****

An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled f(x)= -x^3+21x^2+15x units x hours later.

a) Derive a formula for the rate at which the worker will be assembling units after xx hours. r(x)= -3x^2+42x+15

b) At what rate will the worker be assembling units at 9:00 A.M.?

The worker will be assembling 54 units per hour.

c) How many units will the worker actually assemble between 9:00 A.M. and 10:00 A.M.?

The worker will assemble __________ units.