Aprofit -maximizing firm has the total-cost function c= x^2 + 2x and sells into a competitive market on which the price is $10. what output should it produce?

hint: find the derivative and check for local maxima and minima

The output produce is 4.

Step-by-step explanation:

Given : A profit -maximizing firm has the total-cost function and sells into a competitive market on which the price is $10.

To find : What output should it produce?  

Solution :

The total-cost function

The revenue function is price into number of item,

So, The revenue function is

The profit function is given by,

The derivative of the profit function,

Equate it to zero to get output,

For maxima/minima we find the second derivative,

As it is a local maxima.

Therefore, The output produce is 4.

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