If the function $f(x) = x^2-2kx+7$ is increasing on [1, 5] then $k$ belongs to

Sand is pouring from a pipe at the rate of 12 $cm^3$/sec. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm ?

The demand for a certain product is represented by the function $p = 300 + 25x - x^2$ (in rupees), where x is the number of units demanded and p is the price per unit, then the marginal revenue when 15 units are sold, is

The interval(s), where the function $f(x) = \begin{cases} \frac{1-e^x}{e^{2x}-1} & : x \neq 0 \\ \frac{-1}{2} & : x = 0 \end{cases}$ is increasing, is/ are:

Function $f(x) = x^x, x > 0$ decreases on the interval

Consider the function $f(x) = x^3 - 3x$. Then

Match List-I with List-II

Choose the correct answer from the options given below:

The function $f(x) = \frac{x - 2}{x + 1}, x \neq -1$ is increasing when (Where $\mathbb{R}$ is a set of real numbers)