(Q2) Consider the graph below of a function f, with a piece missing on the interval (1, 3). Also assume that f extends to -oo and oo along the lines shown. 2 1. 2 4. -1 (a) Suppose that we added a line segment to connect the points (1, 2) and (3, 1) in the given graph. Explain why the resulting function is continuous everywhere. Then find all points where the function is not differentiable. Use definitions appropriately to explain your answers. (b) If the missing piece were such that f was differentiable everywhere instead, show that at some point t in the interval (1,3), the function f has a horizontal tangent line. That is, f'(t) = 0 for some t e (1, 3). (Note: In part (b) you may assume the derivative is 'well-behaved'-that f'(x) is contimuous.)
(Q2) Consider the graph below of a function f, with a piece missing on the interval (1, 3). Also assume that f extends to -oo and oo along the lines shown. 2 1. 2 4. -1 (a) Suppose that we added a line segment to connect the points (1, 2) and (3, 1) in the given graph. Explain why the resulting function is continuous everywhere. Then find all points where the function is not differentiable. Use definitions appropriately to explain your answers. (b) If the missing piece were such that f was differentiable everywhere instead, show that at some point t in the interval (1,3), the function f has a horizontal tangent line. That is, f'(t) = 0 for some t e (1, 3). (Note: In part (b) you may assume the derivative is 'well-behaved'-that f'(x) is contimuous.)
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
Topic Video
Question
Transcribed Image Text:2.
f(z) has a horizontal asymptote: y
(Q2) Consider the graph below of a function f, with a piece missing on the interval (1,3). Also assume
that f extends to -0o and oo along the lines shown.
2
3
4
-1
(a) Suppose that we added a line segment to connect the points (1, 2) and (3, 1) in the given graph.
Explain why the resulting function is continuous everywhere. Then find all points where the
function is not differentiable.
Use definitions appropriately to explain your answers.
(b) If the missing piece were such that f was differentiable everywhere instead, show that at some
point t in the interval (1,3), the function f has a horizontal tangent line. That is, f'(t) = 0 for
some te (1,3).
(Note: In part (b) you may assume the derivative is 'well-behaved'-that f'(x) is continuous.)
MacBook Air
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 3 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.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