4. Below are the graphs of a position function, s(t), a velocity function, v(t), and an accelerationfunction, a(t), with respect to time, t.BB0.50.5dr rateaphofAD4 I can use the first and second derivatives to describe the behavior of functions, includinglisting intervals of increasing/decreasing, concavity, extreme values.i. List the a values where Graph A is neither increasing nor decreasing. (estimate the avalues to 1 decimal place.)ii. List the intervals where Graph A is increasing. (estimate the r values to 1 decimal place.)e (CIRCLE OAiii. List the intervals where Graph A is decreasing. (estimate the r values to 1 decimalplace.)iv. On which intcrvals would A's derivative be positivc?v. Which graph has a second derivative that must be always positive? How do you know?

Answered: 4. Below are the graphs of a position…

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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4. Below are the graphs of a position function, s(t), a velocity function, v(t), and an acceleration
function, a(t), with respect to time, t.
B
B
0.5
0.5
dr rateaphof
A
D4 I can use the first and second derivatives to describe the behavior of functions, including
listing intervals of increasing/decreasing, concavity, extreme values.
i. List the a values where Graph A is neither increasing nor decreasing. (estimate the a
values to 1 decimal place.)
ii. List the intervals where Graph A is increasing. (estimate the r values to 1 decimal place.)
e (CIRCLE OA
iii. List the intervals where Graph A is decreasing. (estimate the r values to 1 decimal
place.)
iv. On which intcrvals would A's derivative be positivc?
v. Which graph has a second derivative that must be always positive? How do you know?

Expert Solution

Step 1

The function is neither increasing or decreasing at the maxima or minima.

Graph B represents the first derivative of function given by graph A. So, the maxima, or, minima for graph A occurs when graph B intersects the x-axis.

So, the graph A is neither increasing or, decreasing at $x = 0.3 and x = 1.5$ , which are maxima and minima, respectively.

ii.

The Graph A is increasing on the intervals: $(- \infty, 0.3) and (1.5, + \infty)$ .

iii.

The Graph A is decreasing on the interval: $(0.3, 1.5)$ .

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