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
![**Problem Statement:**
If \( f(6) = 7 \) and \( f'(6) = 4 \), estimate \( f(5.8) \).
**Solution:**
To estimate \( f(5.8) \), we use the linear approximation formula:
\[
f(x) \approx f(a) + f'(a)(x - a)
\]
Given:
- \( a = 6 \)
- \( f(6) = 7 \)
- \( f'(6) = 4 \)
- \( x = 5.8 \)
Substitute the values into the formula:
\[
f(5.8) \approx 7 + 4(5.8 - 6)
\]
Calculate the difference:
\[
5.8 - 6 = -0.2
\]
Then calculate:
\[
f(5.8) \approx 7 + 4(-0.2) = 7 - 0.8 = 6.2
\]
**Estimate:**
\( f(5.8) \approx 6.2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4962ae7-1cb2-4276-8f6a-b9f851b67289%2F536c4c5d-7aff-4390-a4e3-2d5d35fa5d34%2Fg3rnj1r_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
If \( f(6) = 7 \) and \( f'(6) = 4 \), estimate \( f(5.8) \).
**Solution:**
To estimate \( f(5.8) \), we use the linear approximation formula:
\[
f(x) \approx f(a) + f'(a)(x - a)
\]
Given:
- \( a = 6 \)
- \( f(6) = 7 \)
- \( f'(6) = 4 \)
- \( x = 5.8 \)
Substitute the values into the formula:
\[
f(5.8) \approx 7 + 4(5.8 - 6)
\]
Calculate the difference:
\[
5.8 - 6 = -0.2
\]
Then calculate:
\[
f(5.8) \approx 7 + 4(-0.2) = 7 - 0.8 = 6.2
\]
**Estimate:**
\( f(5.8) \approx 6.2 \)
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 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