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At 2:00 p.m. a car's speedometer reads 30 mi/h. At 2:10 p.m. it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h?.
Let v(t) be the velocity of the car t hours after 2:00 p.m. Then v(1/6) - v(0)
1/6 - 0
By the Mean Value Theorem, there is a number c such that 0 <cs
with
v'(c) =
Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 p.m. is exactly 120 mi/h?.

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