Class 12 Mathematics - Chapter Application of Derivatives NCERT Solutions | The total cost C (x) in Rupees associate
The total cost C (x) in Rupees associated with the production of x units of an item is given by
C(X) = 0.007 x3 - 0.003x2 + 15x + 4000
Find the marginal cost when 17 units are produced.
Marginal cost is the rate of change of total cost with respect to output.
∴Marginal cost
\begin{align}MC=\frac{dC}{dx}=0.007 (3x^2) - 0.003(2x) + 15\end{align}
MC = 0.021 x2 - 0.006x + 15
When x = 17, MC = 0.021 (172) − 0.006 (17) + 15
= 0.021(289) − 0.006(17) + 15
= 6.069 − 0.102 + 15
= 20.967
Hence, when 17 units are produced, the marginal cost is Rs. 20.967.
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