Have you seen this puzzle?
A monk climbs from the base of a mountain to its top on the one narrow path up and down, sleeps in a hut at the top, and then descends again to her monastery the next day. She leaves at about 6am on both days, and arrives around 6pm on both days. She stops for a break whenever she feels like it.
Will there be a time of day where she’s at the same spot on both days?
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I think you can prove this is true using the Intermediate Value theorem.
ReplyDeleteDavid, I think you could convince a good calculus student with the IVT, but a picture is much better on a pre-calc student. For calculus students, perhaps a better question would be to ask if the conditions for the IVT are present .
ReplyDeleteI posted this because I wanted to talk about the IVT in class, and was unsure whether I could get to anything not public on the system. Turned out I couldn't get on the system at all, so I just drew the mountain and its path, and told the story. I gave them a few minutes, and most had no idea. I drew the distance along the path as a function of time, up in blue, down in red. They go it. I talked about what if a helicopter took the monk a ways down the trail, and connected that with continuity.
ReplyDeleteI used this to show what the IVT can do for us.
Why do we care about the IVT in Calc I? It feels like one of a number of random topics thrown in.