`f(x) = 5 - | x- 5|` Find the critical numbers, open intervals on which the function is increasing or decreasing, apply first derivative test to identify all relative extrema.
This function is continuous everywhere and is differentiable everywhere except x=5.
For x<=5, f(x)=x, f'(x)=1 and for x>-5 f(x)=10-x, f'(x)=-1. So there are no points for which f'(x)=0, and x=5 is the only critical point.
The function f is increasing on `(-oo, 5)` and is decreasing on `(5, +oo)` . So x=5 is a relative maximum.