Are the Rocky Mountains higher or the Appalachian Mountains higher?

The rockies are much higher. the highest point in the Appalachian is in NC Mount Mitchell - 6,684 feetwhile the highest point in the Rocky mountains is in Colorado Mount Elbert - 14,433 feet

But this is not the highest point in the lower 48. That would be in the sierra Nevada range in California Mount Whitney - 14,494 feet