Question 630566
If a car traveled 80 miles between 2pm and 4pm. Is it true thst there must have been a time which its instantaneous speed was exactly 40 miles per hour? Justify your answer with an appropriate theorem or a counterexample if false. 
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His average speed was 40.  
Either he maintained 40 for 2 hours,
or he went slower for a time, then faster
for a time.
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In either case there was an instant when his
speed was 40 mph.
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Cheers,
Stan H.