Yes, POSITIVEST is a Scrabble word!

Letter values in Scrabble US: P 3, O 1, S 1, I 1, T 1, I 1, V 4, E 1, S 1, T 1.

Is it a valid word?

POSITIVEST is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

characterized by or displaying affirmation or acceptance or certainty etc.
persuaded of; very sure
involving advantage or good
indicating existence or presence of a suspected condition or pathogen
formally laid down or imposed
impossible to deny or disprove
of or relating to positivism
reckoned, situated or tending in the direction which naturally or arbitrarily is taken to indicate increase or progress or onward motion
greater than zero
having a positive charge
marked by excessive confidence

Also: incontrovertible, positively charged.