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The total cost C(x) in Rupees, associated with the production

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The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 5000$ . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

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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) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 5000

. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

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Text solutionVerified

Solution:

C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 5000

\frac{d ( c x )}{d x} = \frac{d ( 0.005 x ^{3} )}{d x} - \frac{d ( 0.02 )}{d x} + \frac{d ( 30 )}{d x} + 0

= 0.005 (3 x^{2}) - 0.02 (2 x) + 30 \times 1

= 0.005 (3 \times 9) - 0.02 (2 \times 3) + 30

= 0.135 - 0.012 + 30

= 30.015

\frac{d c}{d x} = 30.015

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Question Text	The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 5000$ . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.
Answer Type	Text solution:1
Upvotes	150

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x)=0.005x3−0.02x2+30x+5000. Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

Text solutionVerified

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The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C (x) = 0.005 x^{3} - 0.02 x^{2} + 30 x + 5000$ . Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.