Which of the following statements are true?

(A) The break-even point is the level of production where the revenue from sales is equal to the cost of production and marketing.

(B) If R is the total revenue collected by a company when it sells $x$ units of a product at a price of p per unit, then R is given by $R=px$.

(C) Let $C=C(x)$ be the total cost of producing and marketing $x$ units of a product, then marginal cost, $MC=\frac{dC}{dx}$.

(D) If AC is the average cost, then $AC=\frac{x}{C}$.

Choose the correct answer from the options given below:

The relation between 'marginal cost (MC)' and 'average cost (AC)' of producing 'x' units of a product 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 :

If $y = \log_3(\log_3 x)$, then $\frac{dy}{dx}$

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

Any function f(x) is an increasing function in [a,b] if :

(A) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 < x_2$

(B) $x_1, x_2 \in [a, b], f(x_1) \geq f(x_2)$ if $x_1 > x_2$

(C) (A) $x_1, x_2 \in [a, b], f(x_1) \leq f(x_2)$ if $x_1 < x_2$

(D) (A) $x_1, x_2 \in [a, b], f(x_1) < f(x_2)$ if $x_1 > x_2$

If $x = 2at, y = at^2$, where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :