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.
Next hint
Answer