In the interval $(-3,3)$,the function $f(x) = \frac{x}{3} + \frac{3}{x}, x \neq 0$ is :

If $f(x)=\sqrt{3} \sin x-\cos x-2 a x+b$ decreases for all values of $x$,then

The set of all points,for which $f(x) = x^2 e^{-x}$ strictly increases,is

If $f(x) = x^2 + kx + 1$ is an increasing function on the interval $[1, 2]$,what is the minimum value of $k$?

The function $f(x)=2 x^3-9 x^2+12 x+29$ is monotonically increasing in the interval

Which statement among the following is true?
$(i)$ The function $f(x) = x|x|$ is strictly increasing on $R - \{0\}$.
$(ii)$ The function $f(x) = \log_{(1/4)} x$ is strictly increasing on $(0, \infty)$.
$(iii)$ $A$ one-one function is always an increasing function.
$(iv)$ $f(x) = x^{1/3}$ is strictly decreasing on $R$.