It is tricky as @Sam_SAS notes but it can be done. The overall process would look something like this:
1. Create your slider as normal
2. Create a calculated item using the TreatAs function to convert the Date to a numeric value. This is necessary to make sure parameters get set correctly later.
3. Change the default aggregation of this calculated item to Average instead of the default Sum.
4. Add two drop down lists, both with the same Date item as your slider.
5. For both drop down list options, set it to Required.
6. For both drop down lists, add a new parameter. One parameter is Minimum Date, the other parameter is Maximum Date.
7. For the drop down list that represents Minimum Date, set a Rank with Bottom Count of 1 and the By your Date Numeric calculated item.
8. For the drop down list that represents Maximum Date, set a Rank with Top Count of 1 and By your Date Numeric calculated item.
9. Create a filter interaction from the slider to both drop down lists.
The end result is as you change the slider, the drop down lists get updated to the respective min/max values and get set in the parameters. Then you can use the parameters however you'd like. You can also hide the drop down lists via a precision container if you'd like.
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