 Hello and how are you all today? The question says if the marginal revenue function for a commodity is MR is equal to 9 minus 6x square plus 2x, find the total revenue function and the corresponding demand function. So let's proceed with the solution. We have the marginal revenue function equal to 9 minus 6x square plus 2x. Now with the help of this marginal revenue function we can easily find out the revenue function. Revenue function is found out by integrating the marginal revenue function with respect to x and adding the constant of integration to it. That is equal to integral 9 minus 6x square plus 2x dx plus c which is further equal to 9x minus 6x cube upon 3 plus 2x square upon 2 plus c. On simplifying it we have the revenue function as 9x minus 2x cube plus x square plus. Now we need to find out this constant for integration. We know that when we are not reducing any units then we are not earning any revenue. So this means 0 is equal to 9 into 0 plus 2, sorry minus 2 in place of x we will substitute 0. 0 cube plus 0 square plus c. So this implies the value of c is also equal to 0. So we can write down the revenue function as 9x minus 2x cube plus x square. So here this is our total revenue function and we need to find out the demand function also. Demand function is found out by dividing the revenue function by x. That is 9x minus 2x cube plus x square upon x which is equal to 9 minus 2x square plus x. So the required answer to the session is firstly I am writing down the total revenue function that is 9x minus 2x cube plus x square and then the demand function that is 9 minus 2x square plus x. So these are the answer to the given question. So hope you understood it well and enjoyed it too. Have a very nice day ahead.