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 27:**
The graph of a function \( f \) is given.
Let \( F(x) = \int_{0}^{x} f(t) \, dt \) then for \( 0 < x < 2 \), \( F(x) \) is:
- [A] increasing and concave up
- [B] increasing and concave down
- [C] decreasing and concave up
- [D] decreasing and concave down
**Graph Explanation:**
The graph provided shows the function \( f(t) \), with axes labeled as \( t \) for the horizontal axis and \( f(t) \) for the vertical axis. The graph is a parabolic curve that peaks and then decreases, resembling an inverted U-shape.
The curve:
- Begins at the origin and increases until it reaches a maximum point slightly before \( t = 1 \).
- After the maximum point, the curve decreases, reaching zero slightly before \( t = 3 \).
- This curve demonstrates where the function \( f(t) \) is positive and increasing, then negative and decreasing beyond its peak.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ef4066a-09c4-44d3-9899-dbf8cf9ac919%2F0a622692-8361-4a96-ab06-18f68c4e3cdc%2Finnb0ch_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 27:**
The graph of a function \( f \) is given.
Let \( F(x) = \int_{0}^{x} f(t) \, dt \) then for \( 0 < x < 2 \), \( F(x) \) is:
- [A] increasing and concave up
- [B] increasing and concave down
- [C] decreasing and concave up
- [D] decreasing and concave down
**Graph Explanation:**
The graph provided shows the function \( f(t) \), with axes labeled as \( t \) for the horizontal axis and \( f(t) \) for the vertical axis. The graph is a parabolic curve that peaks and then decreases, resembling an inverted U-shape.
The curve:
- Begins at the origin and increases until it reaches a maximum point slightly before \( t = 1 \).
- After the maximum point, the curve decreases, reaching zero slightly before \( t = 3 \).
- This curve demonstrates where the function \( f(t) \) is positive and increasing, then negative and decreasing beyond its peak.
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 2 steps with 2 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