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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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प्रश्न

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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उत्तर

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

Marginal Cost (MC) =

\[\frac{dC}{dx}\left( x \right) = \frac{d}{dx}\left( 0 . 007 x^3 - 0 . 003 x^2 + 15x + 4000 \right) = 0 . 021 x^2 - 0 . 006x + 15\]

When x = 17,
Marginal Cost (MC) =

\[= 0 . 021 \left( 17 \right)^2 - 0 . 006(17) + 15 = 6 . 069 - 0 . 102 + 15 =\text {  Rs }20 . 967\]
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अध्याय 12: Derivative as a Rate Measurer - Exercise 13.1 [पृष्ठ ४]

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आर.डी. शर्मा Mathematics Volume 1 and 2 [English] Class 12
अध्याय 12 Derivative as a Rate Measurer
Exercise 13.1 | Q 8 | पृष्ठ ४

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