rate of change

[rajendrarama]

The installation of a new electrical component into an existing product on an assembly line has an associated cost(per component), C dollars that is closely approximated by the function
C= 8((1.5t+11.5)^4)^(1/3) '0' less than or equal to 't' less than or equal to '7'

where 't' is measured in years
a) what will be the initial cost per component be?
b) Find the average rate at which the cost per component is changing over the first seven years
c) Find the rate of change in cost per component after 4 years of operation

could anyone please help. I could not able to differentiate

 

[rajendrarama]

yes, that's the one

 

[rajendrarama]

So, dC/dt = 16 (1.5t +11.5)^1/3

a) initial cost would be when t=0,
so, will it be 16(11.5)^(1/3)

b) average rate changing over 7 years
does it mean, I should calculate for t=0, 1,2,.....7 in the above equation
and take the average of it

c) rate of change after 4 years of operation
if I substitute t=4 in the above equation, will it give the answer?


Could you please confirm my analysis?

Thanks in advance

 

[rajendrarama]

Thank you very much

 

[DrPhil]

b) average rate changing over 7 years
does it mean, I should calculate for t=0, 1,2,.....7 in the above equation
and take the average of it

I think part b means [C(7) - C(0)]/7