Question

Suppose that the cost of producing n pairs of shoes is given by the expression c(n)=30+5n. the average cost of producing a pair of shoes is given by a(n)=c(n)/n. what is the derivative of the average cost function at n=10?

Answer 1

Given

`c(n)=30+5n\\a(n)=(c(n))/(n)`

Find

`(d)/(dn)(a(n))\quad\text{at n=10}`

Solution

`(d)/(dn)(a(n))=(d)/(dn)\left((30+5n)/(n)\right)=(d)/(dn)\left(30n^(-1)+5\right)\\\\=-30n^(-2)\\\\=-30\cdot 10^(-2)\qquad\text{at n=10}\\\\=-0.30`

The derivative of the average cost function at n=10 is -0.30.