Find the marginal revenue if the revenue function for a product is R(x)=(60x^2)/2x+1

1 Answer

ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

Posted on

Marginal revenue is defined as a derivative of the revenue function,

`R(x) = (60x^2)/(2x + 1)`

To find the derivative of this function, use the quotient rule:

`(f/g)' = (f'g - fg')/g^2`

The number 60 in the numerator is the constant, so we can just keep it in front of the expression while taking the derivative:

`R'(x) = 60 [2x(2x + 1) - x^2(2)]/(2x + 1)^2 = 60 (4x^2 + 2x - 2x^2)/(2x + 1)^2`

Combining like terms in the numerator and then multiplying by 60, we get

`R'(x) = 60 (2x^2 + 2x)/(2x + 1)^2 = (120x^2 + 120x)/(4x^2 + 4x + 1)`

So the marginal revenue function is

`R'(x) = (120x^2 + 120x)/(4x^2 + 4x + 1)`