Practice question · Multiple choice
A speed camera pair times a car between two points and issues a ticket for exceeding the limit somewhere between them, without observing the speedometer. Which theorem licenses that?
Hints
- Average speed is total distance over total time. Ask what the theorem says about that number.
- You covered 20 km in 8 minutes. Was there a moment at 150 km/h?
Show the answer
D. The Mean Value Theorem, so the average is attained at some instant
Why
Average speed must be attained instantaneously at some point in between, so the ticket follows from the arithmetic without anyone seeing the dial. Average-speed enforcement is a mathematical theorem installed on a motorway, one of the few places the Mean Value Theorem is applied to you directly.
Practise Taylor Approximation
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