Geriatric means of very old people and their medical care. A clinical word, and an insult when it escapes the clinic.
Geriatric medicine is a real and demanding specialism dealing with the particular ways illness presents in old age. The word is entirely neutral there. Used about a person outside medicine it is offensive, and used about an object it is mocking, so a geriatric photocopier is one nobody has replaced. Many hospitals now say care of the elderly precisely to avoid the second sense.
1adjectivegeriatricRelating to the medical care of old people.
“She works on the geriatric ward at the county hospital.”
From geriatrics. by surface analysis, γῆρας + -iatric.
Etymology from Wiktionary, CC BY-SA