If $f(x) = x^3 - 6x^2 + 9x + 3$ is a monotonically decreasing function,then $x$ lies in:

If $f(x) = kx^3 - 9x^2 + 9x + 3$ is monotonically increasing in each interval,then

The number of real roots of the equation $x^5+3x^3+4x+30=0$ is

If a function $f(x)$ is increasing in an interval $x \in [a, b]$,then which of the following will always be correct?

If $5 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0$ and $y=9 x^2 f(x)$,then $y$ is strictly increasing in :

If the tangent drawn to the curve $y=x^3-ax^2+x+1$ at each point $x \in R$ is inclined at an acute angle with the positive direction of the $X$-axis,then the set of all possible values of '$a$' is