18: Derivative is

f ′(x) = 1 + sin(x).

Critical points: f = 0 for x = −π/2 + kπ; there are no points in D( f ) where f ′ does not exist.

Since f ′(x) ≥ 0 is always true, f is non-decreasing on ℝ. Moreover, with the exception of the critical points above, f ′(x) > 0, so in fact f is increasing on ℝ.

There are no local extrema, we just have horizontal tangent lines at the critical points.

Now determine concavity using f ′′.

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