The total cost C (x) associated with the production of x units of an item is given by $C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000.$ Find the marginal cost when 17 units are produced.

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Solution

We have,
$C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000$
$\frac{d}{d x} (C (x)) = 0.021 x^{2} - 0.006 x + 15$
$∴ {(\frac{d}{d x} C (x))}_{x = 17} = 0.021 \times 17^{2} - 0.006 \times 17 + 15$
Hence, marginal cost $= R s 20.967$

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The total cost C(x) in rupees associated with the production of x units of an item is given by $C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000$ .

Find the marginal cost when x=17 units are produced.

The total cost C (x) in Rupees associated with the production of x units of an item is given by

Find the marginal cost when 17 units are produced.

C (x)

x

C (x) = 0.007 x^{3} - 0.003 x^{2} + 15 x + 4000

x = 17.

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