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16. A particle starts at t = 0 and moves along the r-axis so that its position at any time t 20 is given by r (t) = (t – 1)* (2t – 3). a) Find the velocity function v (t) of the particle. b) For what values of t is the object moving to the left? c) Find all values of t for which the object is moving and but its acceleration is zero.

16. A particle starts at t = 0 and moves along the r-axis so that its position at any time t 20 is given by r (t) = (t – 1)* (2t – 3). a) Find the velocity function v (t) of the particle. b) For what values of t is the object moving to the left? c) Find all values of t for which the object is moving and but its acceleration is zero.

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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Question 16

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r COS r * O M A 44% r) redr 7:38 PM w/4 -2 da m) tan z dr re¯*dx sample4Main_7.. Last revised: May 7, 2021 Math 207 Final Review page 3 14. Let f be a function given by f (x) = In a) Find the domain of f. c) Find the formula for the inverse of f. b) Find the value of the derivative of f at r = -1. 15. We are on the surface of the Moon. The gravitational acceleration there is g = -1.6 A rock is thrown vertically upward, from an initial height of 19.2 m, with an initial velocity of 8. a) Find the velocity function v (t) of the object. b) Find the location function s (t) of the object. c) Find the maximal height that the rock will reach. d) How long until the rock hits the ground? e) What is the velocity of the rock when it hits the ground? 16. A particle starts at t = 0 and moves along the r-axis so that its position at any time t 20 is given by z (t) = (t – 1)* (2t – 3). a) Find the velocity function v (t) of the particle. b) For what values of t is the object moving to the left? c) Find all values of t for which the object is moving and but its acceleration is zero. 17. A function f has derivative f' (r) = -18 (x + 5)* (x + 4)² (x + 2) x® (2 – x)³ (4 – x)². a) Plot the graph of f'. b) Find all critical points of f and classify each of them as a maximum, minimum, or a point of inflection. c) How many points of inflection does f have? 18. Write the equation of the degree 3 polynomial P (x), given that а) Р (0) — -2, P (0) — 3, Р" (0) — 12, and Pi" (0) — -240. b) P has a relative minimum at z = -3 and a relative maximum at z = 1, P (0) = 0, and P (1) = 5. 19. Find an equation for all tangent lines drawn to the graph of 2r2 + y? - 5y - a at a= -2. 20. Graph the location function h (t) of an object if h (0) = 0 and the velocity function, v (t) is given on the graph given. Compute h (2), h (4), h (5), h (7), and h (9). ar + b 21. Let f be the function that is given by f (x) = and that has the following properties. i) The graph of f is symmetric with respect to the y-axis. ii) lim f (x) = 0 iii) f' (1) = -2 a) Determine the values of a, b, and c. b) Write an equation for each vertical and each horizontal asymptote of the graph of f. c) Sketch the graph of f (x). 22. We drop a small object. It has a constant acceleration of –10. At a certain time, the object is observed to be at a vertical position of 475 meters. Three seconds later, it is at 280 meters. At what height did we drop the object? 23. Let f (a) = 2" – 7a4 + 70z + 4. Let g (a) be the inverse of f (x). Find g' (4). Last revised: May 7, 2021 Math 207 Final Review 24. Three sides of a symmetric trapezoid are 1 unit long as shown on the picture. Find the fourth side so that the area of the trapezoid is the greatest. 25. Water is being poured into a container at a rate of 0.9' gallones per minute. a) How much water was poured during the first ten minutes? b) Suppose we never cle the tap. How much water w be poured into the container? mi 26. A town is of a circular shape. The area of the town is growing with a constant 3 - (square mile per year). How
Transcribed Image Text:r COS r * O M A 44% r) redr 7:38 PM w/4 -2 da m) tan z dr re¯*dx sample4Main_7.. Last revised: May 7, 2021 Math 207 Final Review page 3 14. Let f be a function given by f (x) = In a) Find the domain of f. c) Find the formula for the inverse of f. b) Find the value of the derivative of f at r = -1. 15. We are on the surface of the Moon. The gravitational acceleration there is g = -1.6 A rock is thrown vertically upward, from an initial height of 19.2 m, with an initial velocity of 8. a) Find the velocity function v (t) of the object. b) Find the location function s (t) of the object. c) Find the maximal height that the rock will reach. d) How long until the rock hits the ground? e) What is the velocity of the rock when it hits the ground? 16. A particle starts at t = 0 and moves along the r-axis so that its position at any time t 20 is given by z (t) = (t – 1)* (2t – 3). a) Find the velocity function v (t) of the particle. b) For what values of t is the object moving to the left? c) Find all values of t for which the object is moving and but its acceleration is zero. 17. A function f has derivative f' (r) = -18 (x + 5)* (x + 4)² (x + 2) x® (2 – x)³ (4 – x)². a) Plot the graph of f'. b) Find all critical points of f and classify each of them as a maximum, minimum, or a point of inflection. c) How many points of inflection does f have? 18. Write the equation of the degree 3 polynomial P (x), given that а) Р (0) — -2, P (0) — 3, Р" (0) — 12, and Pi" (0) — -240. b) P has a relative minimum at z = -3 and a relative maximum at z = 1, P (0) = 0, and P (1) = 5. 19. Find an equation for all tangent lines drawn to the graph of 2r2 + y? - 5y - a at a= -2. 20. Graph the location function h (t) of an object if h (0) = 0 and the velocity function, v (t) is given on the graph given. Compute h (2), h (4), h (5), h (7), and h (9). ar + b 21. Let f be the function that is given by f (x) = and that has the following properties. i) The graph of f is symmetric with respect to the y-axis. ii) lim f (x) = 0 iii) f' (1) = -2 a) Determine the values of a, b, and c. b) Write an equation for each vertical and each horizontal asymptote of the graph of f. c) Sketch the graph of f (x). 22. We drop a small object. It has a constant acceleration of –10. At a certain time, the object is observed to be at a vertical position of 475 meters. Three seconds later, it is at 280 meters. At what height did we drop the object? 23. Let f (a) = 2" – 7a4 + 70z + 4. Let g (a) be the inverse of f (x). Find g' (4). Last revised: May 7, 2021 Math 207 Final Review 24. Three sides of a symmetric trapezoid are 1 unit long as shown on the picture. Find the fourth side so that the area of the trapezoid is the greatest. 25. Water is being poured into a container at a rate of 0.9' gallones per minute. a) How much water was poured during the first ten minutes? b) Suppose we never cle the tap. How much water w be poured into the container? mi 26. A town is of a circular shape. The area of the town is growing with a constant 3 - (square mile per year). How
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