Let the median of a variable equilateral triangle is increasing at the rate of $2\sqrt{3}$ cm/s. Then the rate at which its each side is increasing is:

The real valued function $f(x) = 12x^\frac{4}{3} - 6x^\frac{1}{3}, x \in [-8, 8]$ has absolute maximum value equal to

Consider the function $f(x) = -2x^3 + 3x^2 + 36x - 15$, then which of the following are TRUE?

A. $f(x)$ increases on $(-2, 3)$

B. $f(x)$ decreases on $(-\infty, -2) \cup (3, \infty)$

C. $f(x)$ increases on $(-\infty, -2) \cup (3, \infty)$

D. $f(x)$ neither increases nor decreases on $(-2, 3)$

Choose the correct answer from the options given below:

If the interval in which f(x) = $\frac{x}{4}$ + $\frac{4}{x}$, x ≠ 0 is strictly increasing is (-∞, a) ∪ (b, ∞), then

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

In which of the following interval, the function $f(x) = \frac{x}{\log x}$ is decreasing?

Which of the following functions are increasing on $x \in \left(0, \frac{\pi}{2}\right)$?

(A) $f(x) = \sin x$

(B) $f(x) = \cos x$

(C) $f(x) = \tan x$

(D) $f(x) = \cos 3x$

Choose the correct answer from the options given below: