6) The stopping distance d of a car driven at velocity v by an unimpaired person on a paved road in good weather is given by the following table. The function d(v), measured in feet, is twice-differentiable with d' (v) > 0. v: velocity (mph) 20 30 40 50 60 70 80 d: stopping distance (feet) 39 75 118 172 230 305 395 a) Find the average rate of change of the stopping distance of the car between 20 and 30 mph. Specify units. b) Estimate d'(78). Be sure to specify units. c) Find h'(v) given that h(v) = e.d(v)
6) The stopping distance d of a car driven at velocity v by an unimpaired person on a paved road in good weather is given by the following table. The function d(v), measured in feet, is twice-differentiable with d' (v) > 0. v: velocity (mph) 20 30 40 50 60 70 80 d: stopping distance (feet) 39 75 118 172 230 305 395 a) Find the average rate of change of the stopping distance of the car between 20 and 30 mph. Specify units. b) Estimate d'(78). Be sure to specify units. c) Find h'(v) given that h(v) = e.d(v)
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:The stopping distance d of a car driven at velocity v by an unimpaired
on a paved road in good weather is
given by the following table. The function d(v), measured in feet, is twice-differentiable with d' (v) > 0.
v: velocity (mph)
20 30 40 50 60 70 80
d: stopping distance (feet) 39 75 118 172 230 305 395
a) Find the average rate of change of the stopping distance of the car between 20 and 30 mph. Specify units.
b) Estimate d'(78). Be sure to specify units.
c) Find h'(v) given that h(v) = e.d(v)
d) Is there some velocity for which the stopping distance is 100 feet? Use the Intermediate Value Theorem to explain
your thinking.
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