Preheat oven to 350 degrees F. Combine rosemary, salt, and pepper; rub half the mixture onto meat. Reserve remaining rosemary mixture. Place beef roast, fat side up, on a rack in a shallow roasting pan. Do not add any liquid. Do not cover. Insert a meat thermometer into center of roast. Roast, uncovered, for 1-1/2 to 2 hours or until thermometer registers 135 degrees F for medium rare, or 2 to 2-1/2 hours or until meat thermometer registers 150 degrees F for medium.
Meanwhile, in a large Dutch oven cook sweet potatoes, turnips, and onions, covered, in boiling water for 3 minutes. Drain. Add garlic, olive oil or cooking oil, and remaining rosemary mixture to vegetables. Toss gently to combine. During last 45 minutes of roasting beef, arrange the vegetables around the meat.
Remove roast from oven. Cover roast with foil; let stand 15 minutes before carving. (The meat's temperature will rise about 10 degrees F while standing.) Carve roast. Serve with roasted vegetables. Makes 8 main-dish servings, plus leftovers.