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
![**Transcription for Educational Website:**
---
Let \( f(x) = |3 - x^2| \). Estimate \( f'(1) \) (Hint: \( h = 0.0001 \)).
**Explanation:**
This exercise asks you to estimate the derivative of a function at a specific point using a small increment, \( h \). The function given is an absolute value function, which can affect the approach to finding the derivative due to potential sharp points. The hint provides a small value for \( h \), suggesting a numerical approximation method, likely the difference quotient:
\[ f'(x) \approx \frac{f(x+h) - f(x)}{h} \]
By substituting \( x = 1 \) and \( h = 0.0001 \), you'll be able to estimate the derivative \( f'(1) \).
---
This transcription can assist students in applying numerical methods to estimate derivatives, particularly when dealing with piecewise-defined functions or functions with absolute values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa32a331a-44ec-4e8d-a40f-5fbd27452f88%2Fe0b3db1d-cd3c-44e0-b9c9-18172f5f5a96%2Fnaabccn_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
Let \( f(x) = |3 - x^2| \). Estimate \( f'(1) \) (Hint: \( h = 0.0001 \)).
**Explanation:**
This exercise asks you to estimate the derivative of a function at a specific point using a small increment, \( h \). The function given is an absolute value function, which can affect the approach to finding the derivative due to potential sharp points. The hint provides a small value for \( h \), suggesting a numerical approximation method, likely the difference quotient:
\[ f'(x) \approx \frac{f(x+h) - f(x)}{h} \]
By substituting \( x = 1 \) and \( h = 0.0001 \), you'll be able to estimate the derivative \( f'(1) \).
---
This transcription can assist students in applying numerical methods to estimate derivatives, particularly when dealing with piecewise-defined functions or functions with absolute values.
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 1 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