Question

Your team discussion should center on how knowledge of first and second derivatives can be used to find the profit (or revenue) maximizing output and the cost minimizing output.

Answer 1

In order to Maximize profit

First Step

Calculate Profit

TR(Total Revenue) - TC(Total Cost) = Profit , label it as equation(1)

Second Step

Find the Derivative of the equation (1) and label it as equation (2)

Third Step

Now put equation (2) equal to Zero to find critical point

Fourth Step

Find Second Derivative using equation(2) and put value of x we found in Third step

Final Step

If the result is less than Zero it means profit is Maximized at that value of x or we can say at units of output.

Cost minimizing output

First Step

Find the derivative of TC(Total cost) function

Second Step

Put the equation after derivative equal to zero to find critical point

Third Step

Find Second Derivative of the equation and put in it value of x we found in second step

Final Step

If the result is more than Zero ,it mean total cost is Minimized at that units of output.