If i am not wrong about what you are looking for then:
you can create range filter dimension in endeca. on which you can apply endeca queries to fetch records set with min/max/between values by using endeca range filter parameter Nf.
range filter dimension is : price
you can fetch records whose price is greater than 10 as:
you can fetch records whose price is less than 10 as:
you can fetch records whose price is between than 10 and 20 as:
you can refer to BasicDevGuid.pdf for more details on this.
Adding an analytics statement to get min and max will accomplish this. If you (or your customer) does not have an analytics license, you have other options like using a dimension that you never make available for navigation (and is always expanded) to get the values.
Could also get there by issuing a couple extra queries (for one record, sort by price descending and then the same with price ascending).
Adding logic to your front end to calculate min/max for a dimension may not work. When you refine/navigate your results, some of the dimension values will become unavailable and therefore your calculation might not give you the real min and max. It will only give you the min/max for that navigation state. You can ofcourse fire a separate query to get all the dimVals for your calculation but that can get hairy. my 2 cents.
BranchBird-Pat's solution would work for getting the exact min and max, but there would be some extra overhead from the multiple queries.
Another option might be to approximate the min and max (assuming you want round numbers) by mapping products into "price bucket" dimensions ($5-$10,$10-$20,..) and using the price bucket refinements returned with the nav state to decide the slider min and max. This option won't give you the exact price, obviously, but it may fit your needs.