Generalized Mean-Value Theorem: Let f and g be two functions, each having a derivative (finite or infinite) at each point of an open interval (a, b) and each continuous at the endpoints a and b. Assume also that there is no interior point a at which both f'(x) and g'(x) are infinite. Then for some interior point c we have f'(c)[g(b) – g(a)] = g'(c)[f(b) – f(a)].
Generalized Mean-Value Theorem: Let f and g be two functions, each having a derivative (finite or infinite) at each point of an open interval (a, b) and each continuous at the endpoints a and b. Assume also that there is no interior point a at which both f'(x) and g'(x) are infinite. Then for some interior point c we have f'(c)[g(b) – g(a)] = g'(c)[f(b) – f(a)].
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 2E
Related questions
Question
130 4
![3. Generalized Mean-Value Theorem: Let f and g be two functions, each having a derivative
(finite or infinite) at each point of an open interval (a, b) and each continuous at the
endpoints a and b. Assume also that there is no interior point r at which both f'(x)
and g'(x) are infinite. Then for some interior point e we have
f'(e)[g(b) – g(a)] = g'(c)[f(b) – f(a)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb6dd0c6-5527-4513-9258-707eb85d4bd1%2F77a8dce5-ae0d-483d-9a84-09e6af61a71b%2Fzgn7fyt_processed.png&w=3840&q=75)
Transcribed Image Text:3. Generalized Mean-Value Theorem: Let f and g be two functions, each having a derivative
(finite or infinite) at each point of an open interval (a, b) and each continuous at the
endpoints a and b. Assume also that there is no interior point r at which both f'(x)
and g'(x) are infinite. Then for some interior point e we have
f'(e)[g(b) – g(a)] = g'(c)[f(b) – f(a)].
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
Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning