Question

Suppose the cost of publishing x books is C(x) = 10000 + 25
`√(x)`, find the marginal cost at x=100 by using the derivative. Compare this with the difference C(101) - C(100).

Answer 1

`(dC)/(dQ) \approx 1.25`,
`C(101)-C(100) = 1.247`,
`\delta = 0.24\,\%`

Explanation:

The marginal cost function is:

`(dC)/(dQ) = 12.5\cdot x^{-(1)/(2) }`

The marginal cost for 100 books is:

`(dC)/(dQ) \approx 1.25`

The difference is:

`C(101)-C(100) = 25\cdot (101^{(1)/(2) }-100^{(1)/(2) })`

`C(101)-C(100) = 1.247`

The relative error is:

`\delta = (|1.25-1.247|)/(1.25)* 100\,\%`

`\delta = 0.24\,\%`