For a real number $a$,if a real-valued function $f(x) = 4x^3 + ax^2 + 3x - 2$ is monotonic in its domain,then the range of $a$ is

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

For what value of $a$ is the function $f(x) = (a + 2)x^3 - 3ax^2 + 9ax - 1$ a decreasing function for all $x \in R$?

Let $f : R \rightarrow R$ be defined as,
$f(x)=\begin{cases}-55 x, & \text{if } x<-5 \\ 2 x^{3}-3 x^{2}-120 x, & \text{if } -5 \leq x \leq 4 \\ 2 x^{3}-3 x^{2}-36 x-336, & \text{if } x>4 \end{cases}$
Let $A=\{ x \in R : f \text{ is increasing} \}$. Then $A$ is equal to :

Let $\phi(x) = f(x) + f(2a - x)$,$x \in [0, 2a]$ and $f^{\prime \prime}(x) > 0$ for all $x \in [0, a]$. Then $\phi(x)$ is

For what values of $K$ is the function $f(x) = x^3 + 6x^2 + (9 + 2K)x + 1$ strictly increasing for all $x \in \mathbb{R}$?