You are driving (too fast) down a straight, country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road tracking vehicle speeds and are in contact with each other. At the first officer’s position, you drive by going 39 miles per hour. At the second officer’s position 63 seconds later, you drive by going 38 miles per hour. The second officer pulls you over and gives you a ticket. Were they justified in giving you a ticket, even though you were not caught speeding?

Hint: refer to the Mean Value Theorem to assist with your justification and reasoning.