3) Suppose that f is a differentiable function with domain [0,5] and f' (3) = 0. True or False: This function must have an extreme value at x = 3. O False O True
3) Suppose that f is a differentiable function with domain [0,5] and f' (3) = 0. True or False: This function must have an extreme value at x = 3. O False O True
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
![**Question 3:**
Suppose that \( f \) is a differentiable function with domain \([0, 5]\) and \( f'(3) = 0 \).
**True or False:**
This function must have an extreme value at \( x = 3 \).
- ○ False
- ○ True
**Explanation:**
This question examines whether having a derivative equal to zero at a certain point necessarily implies that the function has a local maximum or minimum (an extreme value) at that point. Consider the following:
- A function's derivative, \( f'(x) \), at a point equals zero can indicate a local extreme value, but it is not guaranteed. The point could also be an inflection point.
- It's important to verify using additional tests (like the second derivative test) to confirm whether it's an extremum or not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F939f19e0-6626-477a-ba7a-4282434e880a%2F7eacece9-0d6d-49f2-9e40-408267a16623%2F8awrl7s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 3:**
Suppose that \( f \) is a differentiable function with domain \([0, 5]\) and \( f'(3) = 0 \).
**True or False:**
This function must have an extreme value at \( x = 3 \).
- ○ False
- ○ True
**Explanation:**
This question examines whether having a derivative equal to zero at a certain point necessarily implies that the function has a local maximum or minimum (an extreme value) at that point. Consider the following:
- A function's derivative, \( f'(x) \), at a point equals zero can indicate a local extreme value, but it is not guaranteed. The point could also be an inflection point.
- It's important to verify using additional tests (like the second derivative test) to confirm whether it's an extremum or not.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 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