Set oven to 400 degrees.
Wash and cut turnips in half. Rub with olive oil and wrap in aluminum foil. Peel sweet potatoes and rub with olive oil and cover with aluminum foil. Put both into the oven until easily pierced with a fork (about 45 minutes).
To boil, place sweet potato chunks in pan. Cover with water and bring to a boil. Cover pot and simmer until tender, about 15 minutes. Drain pot, then mash sweet potatoes and combine with salt.
For latkes
Heat 3 tablespoons butter in a 10-inch skillet over medium heat. Add sweet potato and cook, stirring until lightly browned, for about 10 minutes.
Add ½ cup breadcrumbs, sage, cinnamon, nutmeg, and cayenne. Cook, stirring, for 1 minute.
Preheat oven to 375 degrees.
Scrub sweet potatoes (or peel if you prefer) and cut into wedges.
Place sweet potatoes in a bowl and add olive oil, salt, and pepper.
Toss until wedges are well coated.