The function $f(x) = \tan^{-1}(\sin x + \cos x)$ is an increasing function in the interval.....

Let $g(x)=3 f\left(\frac{x}{3}\right)+f(3-x)$ and $f^{\prime \prime}(x)>0$ for all $x \in(0,3)$. If $g$ is decreasing in $(0, \alpha)$ and increasing in $(\alpha, 3)$,then $8 \alpha$ is

Let $f(x) = x^3 + 6x^2 + px + 2$. If $f(x)$ is a decreasing function on the interval $(-3, -1)$,then $p = \dots$

Which of the following functions is a strictly increasing function?

The function $f(x) = ax + b$ is strictly increasing for all real $x$ if

If $y = 2x + \cot^{-1} x + \log(\sqrt{1 + x^2} - x)$,then $y$