$f(x) = x^3 - 27x + 5$ is an increasing function,when

The function $f(x) = \cos |x| - 2ax + b$ increases on the entire real line. What is the range of $a$?

If the maximum value of $a$,for which the function $f_{a}(x)=\tan ^{-1} 2 x-3 a x+7$ is non-decreasing in $\left(-\frac{\pi}{6}, \frac{\pi}{6}\right)$,is $\bar{a}$,then $f_{\bar{a}}\left(\frac{\pi}{8}\right)$ is equal to

The interval in which $y=x^{2} e^{-x}$ is increasing is

Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.

On the interval $(1, 3)$,the function $f(x) = 3x + \frac{2}{x}$ is