The total cost C (x) associated with the production of x units of an item is given by C (x) = 0.007x³ − 0.003x² + 15x + 4000. Find the marginal cost when 17 units are produced.

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Solution

Since the marginal cost is the rate of change of total cost with respect to its output,

Marginal Cost (MC) = $\frac{d C}{d x} (x) = \frac{d}{d x} (0.007 x^{3} - 0.003 x^{2} + 15 x + 4000) = 0.021 x^{2} - 0.006 x + 15$
When x = 17,
Marginal Cost (MC) = $= 0.021 {(17)}^{2} - 0.006 (17) + 15 = 6.069 - 0.102 + 15 = Rs 20.967$

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Similar questions

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

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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