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
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.
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.
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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