What type of function is $y = x^4$?

Consider two statements $S_1$ and $S_2$.
$S_1$: If $f(x)$ is a differentiable function with $f'(x) > 0$ in $(a, b)$ and $f(x)$ is increasing in $(a, b)$,then $\frac{f(x)}{f'(x)}$ is also increasing in $(a, b)$.
$S_2$: Both $\sin x$ and $\tan x$ are increasing functions in $(0, \frac{\pi}{2})$.
Which of the following is true?

The interval containing all the real values of $x$ such that the real-valued function $f(x) = \sqrt{x} + \frac{1}{\sqrt{x}}$ is strictly increasing is

The function $f(x) = \tan x - x$ is:

Let $h(x) = f(x) - \{f(x)\}^2 + \{f(x)\}^3$ for every real number $x$,then

In which interval is the function $f(x) = x^2 - x + 1$ not monotonic?