Preheat the oven to 450° F.
Peel carrots and cut into roughly ½-inch pieces. Cut the brussels sprouts in halves. Place both in a bowl and set aside.
Pat the chicken dry with a paper towel and place in a 9x13 inch roasting dish. Tie the legs together with butcher twine (optional) and tuck the wings underneath the bird for roasting.
Place the celery sticks and lemon slices into the empty bird cavity.
In a small bowl, mix the butter, rosemary, garlic powder, ½ teaspoon of salt, and ½ teaspoon pepper together. Mix until well combined.
Using a spoon or basting brush, rub the herbed butter evenly over the chicken skin, and under it.
Place the chopped vegetables in the bottom of the baking dish and drizzle with olive oil and ½ teaspoon of the salt and ½ teaspoon of the pepper.
Roast for 10 minutes, then turn oven down to 350° F. Roast for an additional 1 hour 10 minutes, or until the internal temperature is 160° F, or until the juices run clear when pierced with a knife at the joint between the drumstick and the body.
Let your chicken rest for 10 minutes before slicing. The temperature of the meat will continue to rise. Check the temperature once more before eating to make sure it is at least 165° F.