Question

find the intervals on which f is increasing and decreasing
\[\tan^{-1} x\]

Answer 1

it is increasing on its domain

Answer 2

Differentiate... i.e., Find the derivative of f(x)... It would never be lesser than 0...So always increasing...

Answer 3

domain of \(\arctan(x)\) is \((-\frac{\pi}{2},\frac{\pi}{2})\) as \(x\) goes from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\) \(\tan^{-1}(x)\) goes from \(-\infty\) to \(\infty\)