If a number is drawn at random from the set {$1, 3, 5, 7, \dots, 59$},then the probability that it lies in the interval in which the function $f(x) = x^3 - 16x^2 + 20x - 5$ is strictly decreasing,is

In the interval $(7, \infty)$,the function $f(x) = |x-5| + 2|x-7|$ is:

Consider the following statements $S$ and $R$:
$S: \sin x$ and $\cos x$ are both decreasing functions in the interval $\left( \frac{\pi}{2}, \pi \right)$.
$R:$ If a function $f$ is decreasing in an interval $(a, b)$,then its derivative $f'(x)$ is also decreasing in the interval $(a, b)$.
Which of the following is true?

Find the intervals in which the function $f$ given by $f(x) = x^{3} + \frac{1}{x^{3}}, x \neq 0$ is:
$(i)$ increasing
$(ii)$ decreasing.

The length of the interval in which the function $f(x) = 3 \sin x - 4 \sin^3 x$ is an increasing function is ...

The function $f(x) = x^3 - 3x^2 - 24x + 5$ is an increasing function in the interval given below: