The doctor is using a lot of verbs in the imperative:

Откройте рот, пожалуйста!

Скажите "а-а-а".

Давайте я вас послушаю.

Дышите глубже.

Возьмите градусник!

Купите в аптеке капли от насморка.

Пейте побольше тёплой воды и отдыхайте.

Приходите ко мне.

To form the imperative you have to put the verb in the 1st person singular, for example:

1 читать — я читаю = я чита (й+у)

phonetically Ю after a vowel is a combination of two sounds = (й+у)

We throw away the last sound У, the Й sound remains:

ЧИТАЙ
ЧИТАЙ(ТЕ)

2 писать — я пишу

If in the 1st person singular the verb ends with the У, it will become -И in the imperative:

ПИШИ
ПИШИ(ТЕ)

Well, this is the simplest explanation, of course. In Russian, as always, there’re a lot of different exceptions which, unfortunately, don’t follow the rule!