Question

The cost function of a product is given by C(x) =`x^3/3 - 45x^2 -  900x + 36` where x is the number of units produced. How many units should be produced to minimise the marginal cost?

Answer 1

`C(x) = x^3/3- 45x^2 + 900x + 36`
`(dc(x))/dx = x^2 - 90x - 900=M(x)`

= Marginalcost
`(dc(x))/dx = x^2 - 90x - 900 = M(x)`
                                              = marginal cost
`(d^2c(x))/dx^2 = (2x-90=dM(x))/dx `
 
`therefore (d^2M(x))/dx^2 = 2 > 0`

`therefore (dM(x))/dx ` is minimum
To be minimum
`(dM(x))/dx =0`
2x - 90 =0
2x = 90
x= 45