When in a calender view, you can also create a task for a specific date. Click on Calendar tab as below.
Click on any day or time interval depending your current calendar view. The Event | Task window appears. By default, the Event link is selected. Click on Task link and you can see the following.
In Due On field, you can see that the due date or time of new task is selected by default, depending on where you clicked in the calendar view.
Click on Clear Date and Time button, to clear these date and time values or to specify your custom date and time values. You can also change the date and time values without clearing the default values.
To see more details on how to create this new task, please see add new task.