List of top Mathematics Questions on Increasing and Decreasing Functions asked in CBSE Class XII

Find the interval(s) in which the function $f(x) = \frac{x}{\log x}$, where $x \in (0, 1) \cup (1, \infty)$, is increasing.

Find the sub-intervals of \[ (0,\pi) \] in which \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

Find the sub-interval of \[ (0,\infty) \] in which \[ f(x)=x^2e^{-x} \] is increasing.