Place the pork tenderloin in a 10x15 inch roasting pan. In a separate small bowl, combine the garlic, ground black pepper, tarragon and olive oil. Mix this well and spread over the pork. Then place the carrots and potatoes around the meat. Combine the soy sauce and 1 cup water in a separate small bowl and pour over the vegetables around the roast. Cover all tightly with foil.
Bake at 350 degrees F (175 degrees C) for 1 to 1 1/2 hours, or until the internal pork temperature reaches 145 (63 degrees C).
Transfer the roast and vegetables to a serving platter and pour the liquid from the roasting pan into a small saucepan over medium heat. In a separate small bowl, dissolve the cornstarch in the remaining 1/2 cup water and add to the liquid in the pan. Stir well and allow sauce to thicken.