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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

Respuesta :

We can replace x=20000 in the function so:

[tex]c(20000)=15000+8(20000)-\frac{20000^2^{}}{20000}[/tex]

and we simplify:

[tex]c(20000)=15500[/tex]

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

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

So for h=1 will be :

[tex]C=0.599950[/tex]

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