 Hi and welcome to the session. Let's work out the following question. The question says the cost function of a firm is given by cx is equal to 300x minus 10x squared plus x cubed by 3. Calculate the output at which marginal cost is minima. Also calculate the minima marginal cost. So let us see the solution to this question. Now here c is equal to 300x minus 10x squared plus x cubed by 3. We know that the marginal cost or we can say mc is equal to derivative of the cost function with respect to x that is equal to 300 minus 20x plus x squared. Now derivative of marginal cost with respect to x will be equal to minus 20 plus 2x now for maximum or minimum values derivative of marginal cost with respect to x should be equal to 0. This implies 2x minus 20 should be equal to 0. This further implies that x is equal to 10. Now second derivative of marginal cost with respect to x is equal to 2 which is positive. Now this we find out at x equal to 10 since this is positive therefore mc or the marginal cost is minimum when x is equal to 10. Also the minimum value of marginal cost at x equals to 10 will be 300 minus 20 into 10 plus 10 squared that is equal to 300 minus 200 plus 100 that is equal to 100 plus 100 and that is equal to 200. So our answer to this question is that the output at which marginal cost is minimum is x equal to 10 and the minimum marginal cost is 200. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.