Posted by smith lionel on Friday, January 13, 2012 at 11:55am.
An automobile travels 4 miles road in 5 minutes. Use the Mean Value theorem to show that the speedometer reads exactly 48 mph at least once during the trip.

calculus  Steve, Friday, January 13, 2012 at 1:00pm
MVT states that for an interval [a,b] there is a c such that f'(c) = (f(b)f(a))/(ba)
Here letting f(x) be distance at time x minutes,
f(0) = 0
f(5) = 4
(f(5)f(0))/(50) = 4/5 mi/min (that's 48 mph)
MVT states that at some 0<= c <= 5, f'(x) = 4/5
f'(x) is the speedometer reading at x minutes.
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