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Question 2. In this problem we give another characterization for the average function value introduced in lecture. Let a < b be constants and let f be an integrable function. Consider the function F :R → R, defined by F(x) = | (f(t) – x)² dt. dF (1) Find the critical point(s) of F (i.e., the point(s) where dr 0). (2) On such critical point (s) does the function F achieve a minimum, maximum, or neither?

Question 2. In this problem we give another characterization for the average function value introduced in lecture. Let a < b be constants and let f be an integrable function. Consider the function F :R → R, defined by F(x) = | (f(t) – x)² dt. dF (1) Find the critical point(s) of F (i.e., the point(s) where dr 0). (2) On such critical point (s) does the function F achieve a minimum, maximum, or neither?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls help on this question. Also, pls refer to both images to see what needs to be done. 

s for correct computations in part 1. for a correct answer to part 2. for appropriate justification to part 2. for a correct answer to part 3 given in a full sentence.
Transcribed Image Text:s for correct computations in part 1. for a correct answer to part 2. for appropriate justification to part 2. for a correct answer to part 3 given in a full sentence.
Question 2. In this problem we give another characterization for the average function value introduced in lecture. Let a <b be constants and let f be an integrable function. Consider the function F :R → R, defined by F(x) = | (f(t) – x)² dt. a dF (1) Find the critical point(s) of F (i.e., the point(s) where 0). dx (2) On such critical point(s) does the function F achieve a minimum, maximum, or neither? (3) Based on parts 1 and 2, characterize the average function value 1 -I f(t) dt in terms of the function a a F.
Transcribed Image Text:Question 2. In this problem we give another characterization for the average function value introduced in lecture. Let a <b be constants and let f be an integrable function. Consider the function F :R → R, defined by F(x) = | (f(t) – x)² dt. a dF (1) Find the critical point(s) of F (i.e., the point(s) where 0). dx (2) On such critical point(s) does the function F achieve a minimum, maximum, or neither? (3) Based on parts 1 and 2, characterize the average function value 1 -I f(t) dt in terms of the function a a F.
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