Function $f(x) = \frac{|x - 1|}{x^2}$ is monotonically decreasing in

Find the intervals in which the function $f(x) = 6 - 9x - x^{2}$ is strictly increasing or strictly decreasing.

Let $n$ be a natural number and let $a$ be a real number. The number of zeroes of $x^{2n+1} - (2n+1)x + a = 0$ in the interval $[-1, 1]$ is:

For all values of $x$,the function $f(x) = 2x^3 + 6x^2 + 7x - 19$ is:

If $f(x) = \int_{x^2}^{x^2 + 1} e^{-t^2} dt$,then $f(x)$ increases in

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,