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

Let $f(x) = \sin x$ and $g(x) = x$.
Statement $1$: $f(x) \le g(x)$ for $x$ in $(0, \infty)$.
Statement $2$: $f(x) \le 1$ for $x$ in $(0, \infty)$ but $g(x) \to \infty$ as $x \to \infty$.

If $f(x) = \frac{x}{x^2+1}$ is an increasing function,then the value of $x$ lies in:

The values of $a$ for which the function $f(x) = (a + 2)x^3 - 3ax^2 + 9ax - 1$ decreases monotonically for all real $x$ are:

The function $f(x) = \cos |x| - 2ax + b$ increases on the entire real line. What is the range of $a$?

The function $f(x) = \frac{1}{1 + x^2}$ is decreasing in the interval