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Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function h(t)=-4.9t2 + 60t + 5 where h is in meters and t is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time t B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. Using your answer to parts A and B, find the time t that the ball starts falling

Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function h(t)=-4.9t2 + 60t + 5 where h is in meters and t is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time t B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. Using your answer to parts A and B, find the time t that the ball starts falling

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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**Local Extrema, Applied** Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function \[ h(t) = -4.9t^2 + 60t + 5 \] where \( h \) is in meters and \( t \) is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time \( t \) B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. *Using your answer to parts A and B*, find the time \( t \) that the ball starts falling D. Find the height of the ball when it starts falling E. Graph \( h \), and describe what you see relates to your answers to parts A-D F. Now, consider the following prompt: "Find the maximum height of the ball." What we did for parts A-D is actually how we would answer this question. Compare your process for this discussion post to what we learned in section 4.3.
Transcribed Image Text:**Local Extrema, Applied** Next week, we will look at some applications of Local Extrema, but we will do a simple example here that doesn't require much setup. Solve each part, providing explanations wherever necessary. Suppose you throw launch a ball into the air, and its height is given by the function \[ h(t) = -4.9t^2 + 60t + 5 \] where \( h \) is in meters and \( t \) is seconds after you launch the ball. Do the following: A. Find the velocity of the ball at time \( t \) B. At some point the ball is going to start falling back down. What is the velocity of the ball at the moment it stops going up and starts going down? Hint: you should not do any math to answer this part of the question; think about what you would actually see the ball do at this moment. C. *Using your answer to parts A and B*, find the time \( t \) that the ball starts falling D. Find the height of the ball when it starts falling E. Graph \( h \), and describe what you see relates to your answers to parts A-D F. Now, consider the following prompt: "Find the maximum height of the ball." What we did for parts A-D is actually how we would answer this question. Compare your process for this discussion post to what we learned in section 4.3.
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