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Hello thanks for reaching out!
It is possible to create an email notification in settings in automations when a task type is modified.
First create an email template in settings that has some standard language like, "Task has been changed".
Then create an automation in settings. For example, When a task is modified, If task type is equal to "appointment" (modified), require all conditions to be true and add an action to send an email to assignees (with the email template you made).
You may also put an activity report on your custom dashboard that will show changes to a task such as from what older time and date to what newer time and date. Simply add a filter to the activity report and save it (System Activity > Contains > Any > Task Modified).
You may reach out to support for further details. (firstname.lastname@example.org)
Hope that helps.