Question

The average cost function for the weekly manufacture of portable CD players is given by
C(x) = 170,000x−1 + 20 + 0.0008x
dollars per player,
where x is the number of CD players manufactured that week. Weekly production is currently 4,000 players and is increasing at a rate of 300 players per week. What is happening to the average cost?

Answer 1

your formula is broken, re-check it.

Answer 2

C(x) = 170,000^(-1) + 20 + 0.0008x

Answer 3

using chain rule
\[\frac{dC}{dt} = \frac{dC}{dx}*\frac{dx}{dt}\]
\[\frac{dC}{dx} = -170,000x^{-2}+.0008\]
x = 4,000 , dx/dt = 300
\[\frac{dC}{dt} = (-170,000(4000)^{-2} +.0008)*300 = -2.9475\]