Question

ssume that the cost of producing n pair of shoes is given by C(n)=4n(1/2)+3n2. The marginal cost of producing shoes at n is the derivative of C at n. What is the expression of the marginal cost of producing shoes at n?

Answer 1

Answer: The expression of the marginal cost of producing shoes at n would be : $2n^{\frac{-1}{2}}+6n$

Step-by-step explanation:

Given : The cost of producing n pair of shoes is given by  

$C(n)=4n^{\frac{1}{2}}+3n^2$

Since , the  marginal cost of producing shoes at n is the derivative of C at n.

Therefore , Marginal cost function  =  $C'(n)=4 (\dfrac{1}{2}n^{\frac{1}{2}}-1)+3(2n)\ \ [\because\ \dfrac{d\ x^m}{dx}=mx^{m-1}]$

$=2n^{\frac{-1}{2}}+6n$

Hence, the expression of the marginal cost of producing shoes at n would be : $2n^{\frac{-1}{2}}+6n$