In which of the following intervals does $f(x) = 2x^3$ increase less rapidly than $g(x) = 9x^2 - 12x + 6$?

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

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

Find the intervals in which the function $f$ given by $f(x) = x^{3} + \frac{1}{x^{3}}, x \neq 0$ is:
$(i)$ increasing
$(ii)$ decreasing.

If $f(x) = \frac{\log x}{x}$ $(x > 0)$,then it is increasing in

Assertion $(A)$: The function $f(x) = x - \log \left(\frac{1+x}{x}\right), x > 0$ has no maximum. Reason $(R)$: If a function $f(x)$ is strictly increasing in an interval $(a, b)$,then at any point in $(a, b)$,$f^{\prime}(x) \neq 0$. The correct option among the following is