If $f(x) = \frac{\sin x + b \cos x}{\sin x + 4 \cos x}$ is a strictly increasing function,then:

Let the function $f(x) = \frac{x}{3} + \frac{3}{x} + 3$,$x \neq 0$ be strictly increasing in $(-\infty, \alpha_1) \cup (\alpha_2, \infty)$ and strictly decreasing in $(\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5)$. Then $\sum_{i=1}^5 \alpha_i^2$ is equal to :-

For every value of $x \in [1, 3]$,the function $f(x) = \frac{1}{8^x}$ is

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

The value of $k$ such that the function $f(x) = \sin x - \cos x - kx + b$ is strictly decreasing for all real $x$ is

If $f(x) = \frac{k \sin x + 2 \cos x}{\sin x + \cos x}$ is strictly increasing for all real values of $x$,then