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 second order derivative of the function $y=\log(4x^3+6)$ with respect to 'x' will be:

The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$. The output $x$ at which the marginal cost is minimum is :

Let $f : R \to R$ be defined such that $f(x) = 16x^2 - 16x + 12$

(A) Maximum value of $f(x)$ is 8

(B) Minimum value of $f(x)$ is 8

(C) Minimum value of $f(x)$ is 16

(D) No maximum value of $f(x)$

Choose the correct answer from the options given below :

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 :

The demand function for a commodity is $p = 45 + x - x^2$, then the consumer's surplus at equilibrium price $p_0 = 25$ will be:

If $C(x) = x^3 - \frac{5}{2} x^2 + 10$ represents the total cost of producing x unit by car manufacturing company. The slope of the marginal cost curve at $x = 3$, will be