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## Main Question or Discussion Point

The absolute value function [itex] f(x)=|x| [/itex] has a global minimum at x=0. How could we prove this rigorously? In other words, how could we prove that there is no point [itex] c \ \epsilon \ ℝ [/itex] such that [itex] f(c)<f(0) [/itex]

(Obviously, the function is not differentiable at x=0 so we cannot apply Fermat's critical point theorem).

BiP

(Obviously, the function is not differentiable at x=0 so we cannot apply Fermat's critical point theorem).

BiP