Question

Suppose the cost of publishing x books is C(x) = 10000 + 25tle="\sqrt{x}" alt="\sqrt{x}" align="absmiddle" class="latex-formula">, find the marginal cost at x=100 by using the derivative. Compare this with the difference C(101) - C(100).

Answer 1

Answer:

$\frac{dC}{dQ} \approx 1.25$, $C(101)-C(100) = 1.247$, $\delta = 0.24\,\%$

Step-by-step explanation:

The marginal cost function is:

$\frac{dC}{dQ} = 12.5\cdot x^{-\frac{1}{2} }$

The marginal cost for 100 books is:

$\frac{dC}{dQ} \approx 1.25$

The difference is:

$C(101)-C(100) = 25\cdot (101^{\frac{1}{2} }-100^{\frac{1}{2} })$

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

The relative error is:

$\delta = \frac{|1.25-1.247|}{1.25}\times 100\,\%$

$\delta = 0.24\,\%$