# The total cost $C\left ( x \right )$ associated with the production of x units of an item is given by $C\left ( x \right )= 0\cdot 005x^{3}-0\cdot 02x^{2}+30x+5000\cdot$ 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.

cost function is given as
$C\left ( s \right )= 0\cdot 005x^{3}-0\cdot 02x^{2}+30s+5000$
Marginal cost $\left ( MC \right )= \frac{d}{dx}\left ( C\left ( x \right ) \right )$
$= 0\cdot 005\left ( 3x^{2} \right )-0\cdot 02\left ( 2x \right )+30$
$= 0\cdot 015x^{2}-0\cdot 045+30$
when  $x=3, MC= 0\cdot 015\left ( 3 \right )^{2}-0\cdot 04\left ( 3 \right )+30$
$= 0\cdot 135-0\cdot 12+30$
$\Rightarrow 30\cdot 015$

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