Positively

adv.hopeful, kindprofessional

Meaning 1

In a constructive, approving, or favorable way.

Reach for it when describing a beneficial response or effect

The supervisor responded positively to the proposed safety pause.

everyday
optimistically
when hopeful expectation shapes the response
not when Optimism concerns the future, not necessarily current benefit or approval.
warm
approvingly
when visible acceptance from a person is central
not when Approval can reinforce a poor idea and need not be constructive.
professional
beneficially
when the effect produces an advantage
not when The uncommon adverb sounds technical and says nothing about attitude.
professional
constructively
when a response helps improve the situation
not when Constructive criticism may be negative in judgment rather than favorable.
formal
favorably
when an evaluation or comparison supports approval
not when Favorably does not show that the effect itself is beneficial.

With complete certainty or emphatic force.

Reach for it when strengthening a claim in a formal or slightly old-fashioned voice

The second test identified the mineral positively.

everyday
definitely
when certainty needs plain emphasis
not when It can also mean a firm intention and lacks positively's older formal tone.
professional
conclusively
when evidence settles a question
not when Conclusive proof is stronger than confident identification.
formal
unequivocally
when no ambiguity or qualification remains
not when It is too absolute if any uncertainty survives.

respond positively
Most residents respond positively when the reason for a change is visible.
positively affect
The shaded benches positively affect how long older visitors can stay.
positively identify
The conservator could positively identify the pigment after spectroscopy.

The definition and the example on this page are written here. The dictionaries above ground which meaning is being described, not the wording.