22: The domain is given as D( f ) = [0,∞).
The derivative is

Critical points: The equation f ′(x) = 0 has solutions given by the equation 2π/(x + 1) = kπ. This reads x = 2/k − 1. The only integers k that would yield non-negative x are 1 and 2, giving rise to x = 0 and x = 1. Thus there is one critical point x = 1.
There are no points in D( f ) where the derivative does not exist.

Intervals of monotonicity will be [0,1] and [1,∞). Determine monotonicity and local extrema using a chart.

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