This is the question that I just can't get and I reeallly need to: A hiker leaves at 5am, and arrives at his/her destination at 5pm(same day). The hiker then leaves the next day at 5am and arrives at 5pm (same day). Use the intermediate value theorem to show that the hiker arrives at the same point on both days at the same time of day.
How do I do this?
October 16th 2005, 10:23 PM
Represent the route as an interval, say [0,100] representing the percentage of the way along. Assume that the two days walks are continuous functions from [5,17] -> [0,100], say f and g. We have f(5)=0, f(17)=100 and coming back g(5)=100, g(17)=0. You're being asked to show that there exists a t in [5,17] such that f(t) = g(t). Apply the IVT to the function h(t) = g(t) - f(t) which has the property that h(5) = 100, h(17)=-100.