Concept explainers
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
- a. Evaluate f(0), f(2), g(0), and g(2).
- b. Let h(t) = f(t) − g(t). Find h(0) and h(2).
- 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.
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