The marginal cost (MC) of producing x units of an item in a factory is given by $MC=0.006x^2-0.001x+4$.

If the fixed cost is ₹1000, then the cost of producing 200 units will be :

If the cost function and the profit function for a company is given by $C = 10 - 0.3x^2$ and $P = 0.3x^2 + 2x - 10$ respectively , where X represent units of output, then the revenue function is given by :

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$. Which of the following are correct ?

A. 2.6 is the marginal cost when 5 units are produced.

B. $\frac{2x}{25} + 2$ is the marginal cost function.

C. $\frac{x}{25} + 2$ is the average cost function.

D. 2.4 is the marginal cost when 5 units are produced.

E. $\frac{x}{25} + 1$ is the average cost function.

Choose the correct answer from the options given below:

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :

A company is selling a certain commodity $x$. The demand function for the commodity is linear. The company can sell $2000$ units when the price is ₹$8$ per unit and it can sell $3000$ units when the price is ₹$4$ per unit. The Marginal revenue at $x=5$ is:

If $y = x^3 \log x$, then $\frac{d^2 y}{dx^2}$ is equal to :