In the interval $[0, 1]$,the function $f(x) = x^2 - x + 1$ is

If $f(x)=x^3+b x^2+c x+d$ and $0 < b^2 < c$,then in $(-\infty, \infty)$

If the function $f(x) = \cos |x| - 2ax + b$ is an increasing function on the entire real line,then what is the value of $a$?

The function $f(x) = \sin^4 x + \cos^4 x$ is increasing in

The function $f(x)=x^{2}-2x$ is strictly decreasing in the interval

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?