Let C = C(x) be the total cost of producing x units of a product and AC is the average cost and MC is the marginal cost, then

Match List-I with List-II

List-I	List-II
(A) AC decreases with x	(I) when MC = AC
(B) AC increases with x	(II) when MC < AC
(C) AC doesn't change with x	(III) when MC = 0
(D) C is constant.	(IV) when AC < MC

Choose the correct answer from the options given below:

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

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

The second order derivative of which of the following functions is $5^x$ ?

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:

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

If $C(x) = ax^2 - bx - c$ represents the total cost function then the slope of the tangent to the marginal cost curve at the point $(x, y)$ is :