Homework Help is Here – Start Your Trial Now!
Math
Calculus
A function f is defined on an interval [a, b]. Which of the following statement(s) is/are incorrect? (1) If f(a) and f(b) have opposite signs, then there must be a point c E (a, b) such that f(c) = 0. (2) If f is continuous on [a, b), f(a) < 0, and f(b) > 0, then there must be a point c E (a, b) such that f(c) = 0. (3) If f is continuous on [a, b] , and there is a point c in (a, b) such that f(c) = 0. Then f(a) and f (b) have opposite signs. (4) If f has no zeros on la, bl. then f(a) and f(b) have the same sign.

A function f is defined on an interval [a, b]. Which of the following statement(s) is/are incorrect? (1) If f(a) and f(b) have opposite signs, then there must be a point c E (a, b) such that f(c) = 0. (2) If f is continuous on [a, b), f(a) < 0, and f(b) > 0, then there must be a point c E (a, b) such that f(c) = 0. (3) If f is continuous on [a, b] , and there is a point c in (a, b) such that f(c) = 0. Then f(a) and f (b) have opposite signs. (4) If f has no zeros on la, bl. then f(a) and f(b) have the same sign.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.1: Functions
Problem 5E: A Function f is a rule that assigns to each element x in a set A exactly ________ element(s) called...
See similar textbooks
icon
Related questions
Question

Choose all the incorrect answers and explain the same. Please find the question in the image attached.

A function f is defined on an interval [a, b] . Which of the following statement(s) is/are incorrect? (1) If f(a) and f(b) have opposite signs, then there must be a point c e (a, b) such that f(c) = 0. (2) If f is continuous on [a, b], f(a) < 0, and f(b) > 0, then there must be a point c E (a, b) such that f(c) = 0. (3) If f is continuous on [a, b] , and there is a point c in (a, b) such that f(c) = 0. Then f (a) and f(b) have opposite signs. (4) If f has no zeros on [a, b] , then f(a) and f(b) have the same sign.
Transcribed Image Text:A function f is defined on an interval [a, b] . Which of the following statement(s) is/are incorrect? (1) If f(a) and f(b) have opposite signs, then there must be a point c e (a, b) such that f(c) = 0. (2) If f is continuous on [a, b], f(a) < 0, and f(b) > 0, then there must be a point c E (a, b) such that f(c) = 0. (3) If f is continuous on [a, b] , and there is a point c in (a, b) such that f(c) = 0. Then f (a) and f(b) have opposite signs. (4) If f has no zeros on [a, b] , then f(a) and f(b) have the same sign.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Reflections
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
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
SEE MORE TEXTBOOKS