1. What is the first thing to consider when finding the extrema of a function? A. Check the critical points. B. Evaluate x on the given interval. C. Identify the asymptotes. D. Verify whether continuous or not. 2. In what interval does x-4 lie? A. [-2, 4) В. (0, 3] C. [-2, 6] D. [-1, 2] For numbers 3 and 4, study the graph at the right using the interval [-5, 5] 3. What is the maximum point? А. (-3, 2) В. (-1, -3) С. (2, 1) D. (4, -1) (-3,2) (2,1) (4.-1) 4. At what value of x is fminimum? В. 2 D. -3 A. 4 C. -1 (-1-) For numbers 5 and 6, use f(x) -x3- 14x2-60x - 75on the interval [-7, -5]. 5. Which is the absolute minimum? A. (-7,-6) В. (-6, -3) С. (-5, -1) D. (-4, 0) 6. Which is the absolute maximum? A. (-7, 2) В. (-7, 0) С. (-6, 3) D. (-5, 4)
1. What is the first thing to consider when finding the extrema of a function? A. Check the critical points. B. Evaluate x on the given interval. C. Identify the asymptotes. D. Verify whether continuous or not. 2. In what interval does x-4 lie? A. [-2, 4) В. (0, 3] C. [-2, 6] D. [-1, 2] For numbers 3 and 4, study the graph at the right using the interval [-5, 5] 3. What is the maximum point? А. (-3, 2) В. (-1, -3) С. (2, 1) D. (4, -1) (-3,2) (2,1) (4.-1) 4. At what value of x is fminimum? В. 2 D. -3 A. 4 C. -1 (-1-) For numbers 5 and 6, use f(x) -x3- 14x2-60x - 75on the interval [-7, -5]. 5. Which is the absolute minimum? A. (-7,-6) В. (-6, -3) С. (-5, -1) D. (-4, 0) 6. Which is the absolute maximum? A. (-7, 2) В. (-7, 0) С. (-6, 3) D. (-5, 4)
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...
Related questions
Question
![3.
Activity 2: Determine the absolute extrema of the function f(x)
= x - 12x on [0, 4].
Show complete solution using the four steps.
Step 1. Determine if the polynomial is continuous.
Step 2. Find the first derivative and find the critical points.
Step 3. Evaluate the function at the critical points and the endpoints of the interval.
Note only critical value that lie in the given interval.
Step 4. Determine the maximum point (highest value of f(x)) and the minimum point
(lowest value of f(x), if there is any.
Analysis:
Express what you have learned in these lessons/activities by answering the questions below.
1. When can we say that a function or a graph has extrema (both minimum and
maximum value)?
2. How do we identify the minimum and maximum value of the graph of a function
at a given interval?
4. How can we solve optimization problem?
Assessment:
Multiple Choice. Read and analyze each question. If answer is not among the choices, write the
correct one.
1. What is the first thing to consider when finding the extrema of a function?
A. Check the critical points.
B. Evaluate x on the given interval.
C. Identify the asymptotes.
D. Verify whether continuous or not.
2. In what interval does x-4 lie?
A. [-2, 4)
В. (0, 3]
С. [-2, 6]
D. [-1, 2]
For numbers 3 and 4, study the graph at the right using the interval [-5, 5]
3. What is the maximum point?
A. (-3, 2)
В. (-1, -3)
С. (2, 1)
D. (4, -1)
(-3,2)
(4.-1)
4. At what value of x is fminimum?
В. 2
А. 4
С. -1
D. -3
(-1,-3)
For numbers 5 and 6, use f(x) = -x3 – 14x2 -60x – 75on the interval [-7, -5].
5. Which is the absolute minimum?
A. (-7,-6)
В. (-6, -3)
С. (-5,-1)
D. (-4, 0)
6. Which is the absolute maximum?
А. (-7, 2)
В. (-7, 0)
С. (-6, 3)
D. (-5, 4)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19f10092-395c-4699-be27-fd6b11ece81a%2F0dab0200-983d-49a6-beee-52660f35e5f9%2Fyhxu2y7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3.
Activity 2: Determine the absolute extrema of the function f(x)
= x - 12x on [0, 4].
Show complete solution using the four steps.
Step 1. Determine if the polynomial is continuous.
Step 2. Find the first derivative and find the critical points.
Step 3. Evaluate the function at the critical points and the endpoints of the interval.
Note only critical value that lie in the given interval.
Step 4. Determine the maximum point (highest value of f(x)) and the minimum point
(lowest value of f(x), if there is any.
Analysis:
Express what you have learned in these lessons/activities by answering the questions below.
1. When can we say that a function or a graph has extrema (both minimum and
maximum value)?
2. How do we identify the minimum and maximum value of the graph of a function
at a given interval?
4. How can we solve optimization problem?
Assessment:
Multiple Choice. Read and analyze each question. If answer is not among the choices, write the
correct one.
1. What is the first thing to consider when finding the extrema of a function?
A. Check the critical points.
B. Evaluate x on the given interval.
C. Identify the asymptotes.
D. Verify whether continuous or not.
2. In what interval does x-4 lie?
A. [-2, 4)
В. (0, 3]
С. [-2, 6]
D. [-1, 2]
For numbers 3 and 4, study the graph at the right using the interval [-5, 5]
3. What is the maximum point?
A. (-3, 2)
В. (-1, -3)
С. (2, 1)
D. (4, -1)
(-3,2)
(4.-1)
4. At what value of x is fminimum?
В. 2
А. 4
С. -1
D. -3
(-1,-3)
For numbers 5 and 6, use f(x) = -x3 – 14x2 -60x – 75on the interval [-7, -5].
5. Which is the absolute minimum?
A. (-7,-6)
В. (-6, -3)
С. (-5,-1)
D. (-4, 0)
6. Which is the absolute maximum?
А. (-7, 2)
В. (-7, 0)
С. (-6, 3)
D. (-5, 4)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning