Applying the Intermediate Value Theorem Suppose you parkyour car at a trailhead in a national park and begin a 2-hr hike toa lake at 7 a.m. on a Friday morning. On Sunday morning, youleave 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 distancefrom 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 Sundaymorning.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 issome point along the trail that you will pass at exactly thesame time of morning on both days.
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.
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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