Which of the following are correct? (A) The function $f(x) = 3x+12$ is increasing on R. (B) The function $f(x) = e^{2x}$ is decreasing on R. (C) The function $f(x) = x^2-x-1$ is neither increasing nor decreasing on (-1, 1). (D) The function $f(x) = x^3-3x^2+4x$ is increasing on R. Choose the correct answer from the options given below:

If $x$ is real, then the minimum value of $x^2 - 8x + 25$ is

The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% is :

The function $f(x) = x^3 + 2x^2 - 1$ is

(A) increasing in $\left(\dfrac{-4}{3}, 0\right)$

(B) decreasing in $\left(\dfrac{-4}{3}, 0\right)$

(C) increasing in $\left(-\infty, \dfrac{-4}{3}\right)$

(D) increasing in $(0, \infty)$

Choose the correct answer from the options given below:

If the function $f(x) = x^2 - ax - 2$ is strictly decreasing on $(2, 3)$ then $a$ lies in the interval.

If the rate of change of area of a circle is equal to the rate of change of its diameter, then its radius is equal to :

Let $C(x)$ and $R(x)$ be the cost function and the revenue function for $x$ units of a commodity such that marginal cost of producing 2 units is equal to marginal revenue of selling 1 unit. If $C(x) = ax^3 + bx^2 - 12x + 6$ and $R(x) = 100 + 6ax - bx^2$, then which one of the following is TRUE?