MATH 19A Study Guide - Final Guide: Street Light, Hypotenuse, Maxima And Minima
Document Summary
The last four questions are rather di cult, although the hints provided for the rst two essentially give the proof. Solution: the intermediate value theorem states the following. Let f : [a, b] r be a con- tinuous function and i the interval determined by f (a) and f (b). If d i, then there is some c [a, b] such that f (c). (b) a monk leaves his monastery at 4am one day and hikes up a mountain to a sacred cave, taking his usual path. He arrives at the cave the same day and begins to meditate for a week. When nished, he begins to hike down the mountain at 4am and reaches his monastery before nightfall. Prove that there is a location on the monk"s path that he passed at exactly the same time on his ascent and descent.
