# Application Of Derivatives in Commerce and Economics

#### Ansh Agrawal

I couldnt understand this problem. What do we exactly need to do here ? If anyone could help me out... Thanks :

The marginal cost function of manufacturing x units of a commodity is 6 + 10x - 6x^2 . The total cost of producing one unit of the commodity is Rs. 12 . Find the total and average cost function.

Thanks for checking this out.

#### CRGreathouse

Forum Staff
Take the integral to find the total cost, getting total cost = f(x) for some polynomial f(x) with an unknown constant term. Then solve f(1) = 12 to find that constant.

#### Ansh Agrawal

Thanks a lot.. I got your solution but I couldn't understand the second part.. that is after finding the total cost.. Thanks

#### CRGreathouse

Forum Staff
Well, what did you get for the first part?

#### Ansh Agrawal

Well, the first part that m getting is just the integrated part, that comes to 6x + 5x^2 - 2x^3 which is the total cost..

#### Ansh Agrawal

So is this correct ?

6x + 5x^2 - 2x^3 = 12x

or, 6x - 5x^2 + 2x^3 = 0 ?

#### Ansh Agrawal

that is, 2x^2 - 5x + 6 = 0...

I dont know why its getting so tough..though it doesn't seem to be

#### CRGreathouse

Forum Staff
You forgot the constant of integration, which is what lets you solve for f(1) = 12.

okay.. thanks