$f(x) = x^2 - 6x + 10$ is an increasing function in the . . . . . . interval.

Prove that the function $f$ given by $f(x) = \log(\sin x)$ is increasing on $\left(0, \frac{\pi}{2}\right)$ and decreasing on $\left(\frac{\pi}{2}, \pi\right)$.

If $f(x) = x e^{x(1-x)}, x \in R$,then $f(x)$ is

If $f(x) = \int\limits_0^x {{e^t}{{\sin }^{ - 1}}(t - 1)\ln t\,dt}$ for $x > 0$,then:

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

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