Chapter 2.6, Problem 92E

Applying the Intermediate Value Theorem Suppose you park your car at a trailhead in a national park and begin a 2-hr hike to a lake at 7 A.M. on a Friday morning. On Sunday morning, you leave the lake at 7 A.M. and start the 2-hr hike back to your car. Assume the lake is 3 mi from your car. Let f(t) be your distance from the car t hours after 7 A.M. on Friday morning and let $g(t)$ be your distance from the car t hours after 7 A.M. on Sunday morning.

1. a. Evaluate f(0), f(2), g(0), and g(2).
2. b. Let h(t) = f(t) − g(t). Find h(0) and h(2).
3. c. Use the Intermediate Value Theorem to show that there is some point along the trail that you will pass at exactly the same time of morning on both days.