For the function $f(x) = \sin 3x$,where $x \in [0, \frac{\pi}{2}]$,which of the following is true?

Let $f(x) = xe^{x(1 - x)}$. Then $f(x)$ is:

For what values of $x$ is the function $f(x) = x^3 - 3x^2 - 9x + 22$ strictly decreasing?

Let $f : R \rightarrow R$ be a twice differentiable function such that $f^{\prime\prime}(x) > 0$ for all $x \in R$ and $f^{\prime}(a-1) = 0$, where $a$ is a real number. Let $g(x) = f(\tan^{2}x - 2\tan x + a)$, $0 < x < \frac{\pi}{2}$. Consider the following two statements:
$(I)$ $g$ is increasing in $(0, \frac{\pi}{4})$
$(II)$ $g$ is decreasing in $(\frac{\pi}{4}, \frac{\pi}{2})$
Then,

The interval in which the function $f(x) = 2x^2 - \log x$,for $x > 0$ decreases is

If $f(x)=x^3-10x^2+200x-10$,then