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How recent are the derogatories? If you don't get an auto-approval your application will go to a manual review where an underwriter will look over your credit report and those derogatories could be cause for a denial.
I suggest you read the last few pages of <mod edit> for a feel of what can occur.
Mod note: Sorry, links to that site aren't permitted on myFICO. --UB
If you only have one inquiry on your report just apply.