IL The Hiker You are planning a 20-mile hike in the Cascades. The guidebook provides you with a chart, plotting elevation above the trailhead (in feet) as a function of the distance hiked (in miles). This plot is shown and is modeled by the function e(x)=125x²-6.25x¹. s 31-33. Using the graph of e(x), explain in words how the tangent lines to the graph relate to the difficulty of the 34-36. What can you say about the slope of the tangent line at the point of highest elevation on the graph? 37-39. Find the instantaneous rate of change of elevation as a function of x (distance hiked). Include units your answer. 40-42. Determine how far the hiker will have traveled when he reaches the highest point on the trail. teat 5000
IL The Hiker You are planning a 20-mile hike in the Cascades. The guidebook provides you with a chart, plotting elevation above the trailhead (in feet) as a function of the distance hiked (in miles). This plot is shown and is modeled by the function e(x)=125x²-6.25x¹. s 31-33. Using the graph of e(x), explain in words how the tangent lines to the graph relate to the difficulty of the 34-36. What can you say about the slope of the tangent line at the point of highest elevation on the graph? 37-39. Find the instantaneous rate of change of elevation as a function of x (distance hiked). Include units your answer. 40-42. Determine how far the hiker will have traveled when he reaches the highest point on the trail. teat 5000
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:IL The Hiker
You are planning a 20-mile hike in the Cascades. The
guidebook provides you with a chart, plotting elevation above
the trailhead (in feet) as a function of the distance hiked (in
miles). This plot is shown and is modeled by the function.
e(x)=125x²-6.25x³.
2000
31-33. Using the graph of e(x), explain in words how the tangent lines to the graph relate to the difficulty of the
hike
34-36. What can you say about the slope of the tangent line at the point of highest elevation on the graph?
37-39. Find the instantaneous rate of change of elevation as a function of x (distance hiked). Include units
in your answer.
40-42. Determine how far the hiker will have traveled when he reaches the highest point on the trail.
43-45. What is the elevation of the highest point on the trail? Give your answer accurate to the nearest whole
foot
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