Suppose that a particle moves along a horizontal coordinate line in such a way that its position is described by the function s(t) = 3t" – 91² + 3 for 0

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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The Derivative as a Rate of Change.
Suppose that a particle moves along a horizontal coordinate line in such a way that its position is described by the function s(t) = 3t – 9t² + 3 for 0 <t < 3.
%3D
Find the particle's velocity as a function of t:
v(t) = 9? – 181
Determine the open intervals on which the particle is moving to the right and to the left:
Moving right on:
Moving left on: (0,2)
Find the particle's acceleration as a function of t:
a(t) = 181 – 18
Determine the open intervals on which the particle is speeding up and slowing down:
Slowing down on:
Speeding up on: |
NOTE: State the open intervals as a comma separated list (if needed).
Note: You can earn partial credit on this problem.
Transcribed Image Text:The Derivative as a Rate of Change. Suppose that a particle moves along a horizontal coordinate line in such a way that its position is described by the function s(t) = 3t – 9t² + 3 for 0 <t < 3. %3D Find the particle's velocity as a function of t: v(t) = 9? – 181 Determine the open intervals on which the particle is moving to the right and to the left: Moving right on: Moving left on: (0,2) Find the particle's acceleration as a function of t: a(t) = 181 – 18 Determine the open intervals on which the particle is speeding up and slowing down: Slowing down on: Speeding up on: | NOTE: State the open intervals as a comma separated list (if needed). Note: You can earn partial credit on this problem.
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