Construct the graph of a function f that satisfies the following conditions

Question

Construct the graph of a function f that satisfies the following conditions

f´(-2)=0, f´(0)=0, f´(2)=0, f´(x)>0, si 2<|x|, f´(x)<0 si 0<|x|<2

Answer 1

I think it is possible that the statement of the problem contains a typo,

because all the constraints are on f', no constraint on f.

If there is no typo, then there is no function f' satisfying the conditions:

f'(x) < 0 si 0 < |x| < 2

implies

f'(0) < 0

yet another condition requires

f'(0) = 0