Prerequisites: Max out Derrek's level 2 friendship
Reward: None
Unlocks: Derrek level 3 friendship
After a bit of a rocky start your relationship with Derrek has improved quite a bit, and you might as well push things a bit further. Derrek moves around Moonbury a lot, and can be difficult to find. His house, in the north of Moonbury, and the Police Station are your best bets for tracking him down without using your dog. Derrek is an early riser, as well, so you'll likely see him before anyone else if you head towards his home.
Once you've maxed out the second level of your friendship with Derrek Osman will post a notice on the Bulletin Boards of Moonbury, asking Derrek to come meet with him at the Police Station. You can peep on their conversation from 10:00 to 17:00, any day of the week.
Head over to the Police Station at the right time and you'll find Osman impatiently waiting for Derrek to show up. You go looking for him, you find him, Osman chews him out, and you give Derrek a friendly lecture on not overworking his body. The quest ends on amiable terms, and your relationship with Derrek jumps to the next level. Easy peasy.