3.1 Let f(x) be a differentiable function with f(4)= e and f'(4)=-e. Determine the linear approximation of f near x = 4 and use it to approximate f (4.1). Hint: You do not need to find f(x) to answer this question.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
icon
Related questions
Question
3.1 Let f(x) be a differentiable function with ƒ(4)=e and ƒ'(4)=-e. Determine
the linear approximation of f near x = 4 and use it to approximate f(4.1).
Hint: You do not need to find f(x) to answer this question.
3.2 Give an example of a function f(x) defined for all xe R such that f(x) does
not have a linear approximation at x = 0. Show or explain why f(x) does not
have a linear approximation at x = 0.
Transcribed Image Text:3.1 Let f(x) be a differentiable function with ƒ(4)=e and ƒ'(4)=-e. Determine the linear approximation of f near x = 4 and use it to approximate f(4.1). Hint: You do not need to find f(x) to answer this question. 3.2 Give an example of a function f(x) defined for all xe R such that f(x) does not have a linear approximation at x = 0. Show or explain why f(x) does not have a linear approximation at x = 0.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax