Math problem, Help please

Question

An efficiency study of the morning shift at a certain factory indicates that an average worker who arrives on the job at
7:00 A.M. will have assembled

f(x)=−x3+15x^2+15x

 

units xx hours later

 

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

r(x)= 

 

b) At what rate will the worker be assembling units at
8:00 A.M.?

 

c) How many units will the worker actually assemble between
8:00 A.M. and 9:00 A.M. ?

 

Answer 1

a)

 

Take the derivative of f(x).

 

r(x) = f'(x)

 

r(x) = -3x² + 30x + 15

 

 

b)

 

Evaluate  r(1)

 

Since  x=0   means 7AM.

 

 

c)

 

Evaluate  r(2) - r(1).