Class 12

Math

Calculus

Application of Derivatives

The total cost C(x) in Rupees, associated with the production of x units of an item is given by $C(x)=0.005x_{3}−0.02x_{2}+30x+5000$. 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.

$dxd(cx) =dxd(0.005x_{3}) −dxd(0.02) +dxd(30) +0$

$=0.005(3x_{2})−0.02(2x)+30×1$

$=0.005(3×9)−0.02(2×3)+30$

$=0.135−0.012+30$

$=30.015$

$dxdc =30.015$