Question: A car starts at 60 mph, steadily slows down to 20 mph, and then speeds up to 50 mph by the end of 1 h.

A car starts at 60 mph, steadily slows down to 20 mph, and then speeds up to 50 mph by the end of 1 h. The average speed over the whole time is 40 mph.
Draw the positions of cars from the above descriptions of 1-h trips. What speed must the car achieve according to the Mean Value Theorem? What speeds must the car achieve according to the Intermediate Value Theorem?

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