If an object's position is described by \( d(t) = -t^3 + t^2 \) where \( d \) is distance (meters) and \( t \) is time (seconds).![Graph of the function \( d(t) = -t^3 + t^2 \)]Explanation of the Graph:- The graph is a plot of the function \( d(t) = -t^3 + t^2 \).- The horizontal axis represents time \( t \), and the vertical axis represents distance \( d \).- The function has a point of inflection where it changes concavity, roughly around \( t = \frac{1}{3} \).- For \( t < \frac{1}{3} \), the graph is concave up, and for \( t > \frac{1}{3} \), it is concave down.Which of the following describe the behavior of \( d''(t) \)?- \( d''(t) \) is always positive.- \( d''(t) \) is positive when \( d(t) \) is concave up, \( t < \frac{1}{3} \), and \( d''(t) \) is negative when \( d(t) \) is concave down \( t > \frac{1}{3} \).- \( d''(t) \) is positive when \( d(t) \) is concave up, \( t > \frac{1}{3} \), and \( d''(t) \) is negative when \( d(t) \) is concave down \( t < \frac{1}{3} \).- \( d''(t) \) is always negative.

Consider the given function: dt=-t3+t2 Where d is the distance in meters t is the time in seconds.

If an object's position is described by d(t) = - +t² where d is distance (meters) and t is time (seconds). 37 2- 11 -2 -1 -2 Which of the following describe the behavior of d" (t)? O d"(t) is always positive. O d" (t) is positive whend(t) concave up, t <, and d" (t) is negative when d(t) is concave down t > O d"(t) is positive when d(t) is concave up, t> 3, and d" (t) is negative when d(t)is concave down t <3 O d" (t) is always negative.

If an object's position is described by d(t) = - +t² where d is distance (meters) and t is time (seconds). 37 2- 11 -2 -1 -2 Which of the following describe the behavior of d" (t)? O d"(t) is always positive. O d" (t) is positive whend(t) concave up, t <, and d" (t) is negative when d(t) is concave down t > O d"(t) is positive when d(t) is concave up, t> 3, and d" (t) is negative when d(t)is concave down t <3 O d" (t) is always negative.

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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