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(a) Explain in words what the first and second derivatives of position represent. What are their units in this problem? (b) Calculate the position, velocity, and acceleration of the runner at t = 5 seconds. Include the proper units for each. (c) Is the runner's velocity ever zero? Is her acceleration ever zero? If so, calculate these times. (d) What is the runner's velocity at the instant that she passes her home running west? 8. Find the equation of the tangent line to f(x) = x² - 4x³ + 10 at x = 2.

(a) Explain in words what the first and second derivatives of position represent. What are their units in this problem? (b) Calculate the position, velocity, and acceleration of the runner at t = 5 seconds. Include the proper units for each. (c) Is the runner's velocity ever zero? Is her acceleration ever zero? If so, calculate these times. (d) What is the runner's velocity at the instant that she passes her home running west? 8. Find the equation of the tangent line to f(x) = x² - 4x³ + 10 at x = 2.

Calculus: Early Transcendentals
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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7. A jogger is running along the side of a straight east-west highway. Her position (in feet) from her home is given by s(t) = 0.045t³ -0.0023t4, where t is measured in seconds. Positive values of s(t) indicate that she is east of home, while negative values of s(t) indicate that she is west of home. 40 30 20 10 - 10 5 s(t) 10 15 40 t (a) Explain in words what the first and second derivatives of position represent. What are their units in this problem? (b) Calculate the position, velocity, and acceleration of the runner at t = 5 seconds. Include the proper units for each. (c) Is the runner's velocity ever zero? Is her acceleration ever zero? If so, calculate these times. (d) What is the runner's velocity at the instant that she passes her home running west? 8. Find the equation of the tangent line to f(x) = x² - 4x³ + 10 at x = 2.
Transcribed Image Text:7. A jogger is running along the side of a straight east-west highway. Her position (in feet) from her home is given by s(t) = 0.045t³ -0.0023t4, where t is measured in seconds. Positive values of s(t) indicate that she is east of home, while negative values of s(t) indicate that she is west of home. 40 30 20 10 - 10 5 s(t) 10 15 40 t (a) Explain in words what the first and second derivatives of position represent. What are their units in this problem? (b) Calculate the position, velocity, and acceleration of the runner at t = 5 seconds. Include the proper units for each. (c) Is the runner's velocity ever zero? Is her acceleration ever zero? If so, calculate these times. (d) What is the runner's velocity at the instant that she passes her home running west? 8. Find the equation of the tangent line to f(x) = x² - 4x³ + 10 at x = 2.
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