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

Determine the interval(s) in which \(f(x)=5x^{3/2}-3x^{5/2}\), \(x>0\) is increasing.

Find the sub-interval of \((0, \infty)\) in which \(f(x) = x \log x\) is increasing.

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

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.