The cost of manufacturing x cases of fillfluff is C dollars (in thousands), where C(x) = 4 x + 4 sqrt(x) + 5

Monthly production at t weeks is expected to be x = 6400 + 90 t

Write an equation to express rate of change of cost with respect to time:
(dC)/(dt) =

Question

The cost of manufacturing x cases of fillfluff is C dollars (in thousands), where C(x) = 4 x + 4 sqrt(x) + 5

Monthly production at t weeks is expected to be x = 6400 + 90 t

Write an equation to express rate of change of cost with respect to time:
(dC)/(dt) =

anonymous · Answer

i found equation to express manufacturing cost as a function of time:
C(t) =25600+360t+4sqrt(6400+90t)+5

and 

the equation to express marginal cost:
(dC)/(dx) =4+2/sqrt(x)

anonymous · Answer

i agree with c(t)
but i think the derivative is
4 + 8x

did you take the derivative of initial c(x) ?

anonymous · Answer

yes i  took the deriv and plugged x into the values

anonymous · Answer

i see what you  didd -

go back to c(t )  that sqrt is not correct, sorry

c(t) = 25600 + 36t + 6400^2 + 43200t + 81t^2 +5
c't = 36 + 43200 + 162t 
c't = 162t + 43236

your thoughts?