Question

The function gives the cost to manufacture x items. C(x) = 15,000 + 8x - x2 -; X = 20,000 20,000 Find the average cost per unit of manufacturing h more items (i.e., the average rate of change of the total cost) at a production level of x, where x is as indicated a smaller values of h to check your estimates. Round your answers to five decimal places.) h 10 1 Cave 5.99950 5.9995 x Estimate the instantaneous rate of change of the total cost at the given production level x, specifying the units of measurement. c' (20,000) = 6 $/item A Need Help? Read It Watch It

Answer 1

We can replace x=20000 in the function so:

`c(20000)=15000+8(20000)-\frac{20000^2^{}}{20000}`

and we simplify:

`c(20000)=15500`

now h=1 is the cost of one more item so we evaluate for 20001

`\begin{gathered} c(20001)=15000+8(20001)-(20001^2)/(20000) \\ c(20001)=195010 \end{gathered}`

So for h=1 will be :

`C=0.599950`