`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.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

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.