Answer
See below
Work Step by Step
Local minimum: $(-2.2,-37);(0.3,-39);(2.7,-11)$
Local maximum: $(-1.2,1);(1.8,7)$
All zeros can be at $x\approx -2.7, x\approx-1.2,x=-1,x=1.5,x\approx2.4,x=3$
This can be a 6th degree function.
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