He spoke optimistically to the people.
He spoke to the people optimistically.
He optimistically spoke to the people.
Optimistically, he spoke to the people.
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Place adverbs as close as possible to the words they are supposed to modify. Putting the adverb in the wrong spot can produce an awkward sentence at best and completely change the meaning at worst.
Quoting from the following link:
In accordance with the above, the following seem most accurate: