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.

 

 

 

 
 
 
 
 

Answers (1)

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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