Question

The function f defined by :

f(x) = -| x-3| , x ∈ R has a local maxima.

True or false with full explanation

Answer 1

Is well known:

$\forall\ x\in\mathbb{R}\ |x|\geq0\Rightarrow -|x|\leq0$

But $f(3)=-|3-3|=0$ so f has a local maximum at point $3$ .