微積分英翻中問題 (急)20點 翻譯就好不用教我算

An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at 8:0 a.m. will have produced Q(t)=-t三次方 6t二次方 24t units t hours later a. compute the worker`srate production at 11:00 A.M. b. At what rate it the worker`srate of... show more An efficiency study of the morning shift at a certain factory indicates that an average
worker who arrives on the job at 8:0 a.m. will have produced

Q(t)=-t三次方 6t二次方 24t

units t hours later
a. compute the worker`srate production at 11:00 A.M.
b. At what rate it the worker`srate of production changing with respect to time at 11:00 A.M. ?

solution
a. the worker`s rate of production is the first derivative
R(t)=Q`(t)=-3二次方 12t 24
of the output Q(t). the rate of production at 11:00 A.M. (t=3)is
R(3)=Q`(3)=-3(3)二次方 12(3) 24=33
=33units per hour

b.The rate of change of the rate of production is the second derivative
R`(t)=Q"(t)=- 6(3) 12
of the output function. At 11:00 A.M. ,this rate is
R`(3)=Q"(3)=- 6(3) 12= - 6 units per hour per hour
The minus sign indicates that the worker`s rate of production is decreaasing ; that is,
the worker is slowing down.The rate of this decrease in efficiency at 11:00 A.M. is
6 units per hour per hour