. The function f is defined and differentiable on the interval [- 4, 5]. The graph of f shown in the gure has horizontal tangents at x = 0, 2, 3, and 4 . The regions R, S, and T have areas of 12, 15, and 3 espectively. Let g(x) = !A)dt . (-4,1) R a) At what value of x does g(x) have a point of inflection? Justify your answer. b) What is the maximum of g(x)? Show the analysis to support your answer. c) Find lim 4r(2x)+6x 4-x --2
. The function f is defined and differentiable on the interval [- 4, 5]. The graph of f shown in the gure has horizontal tangents at x = 0, 2, 3, and 4 . The regions R, S, and T have areas of 12, 15, and 3 espectively. Let g(x) = !A)dt . (-4,1) R a) At what value of x does g(x) have a point of inflection? Justify your answer. b) What is the maximum of g(x)? Show the analysis to support your answer. c) Find lim 4r(2x)+6x 4-x --2
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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![2. The function f is defined and differentiable on the interval [-4, 5]. The graph of f shown in the
figure has horizontal tangents at x = 0, 2, 3, and 4. The regions R, S, and T have areas of 12, 15, and 3
respectively. Let g(x) = ! f(t)at.
(-4,1)
R
-2
T.
a) At what value of x does g(x) have a point of inflection? Justify your answer.
b) What is the maximum of g(x)? Show the analysis to support your answer.
c) Find lim (2)=6x
4-x
x--2
d) Let h(x) = : Find h'(- 2).
g(x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee043644-8c82-4555-bd39-471becdabd6c%2Fe191dfce-7b59-4ea0-a02a-70eefcc28711%2Fahved3_processed.png&w=3840&q=75)
Transcribed Image Text:2. The function f is defined and differentiable on the interval [-4, 5]. The graph of f shown in the
figure has horizontal tangents at x = 0, 2, 3, and 4. The regions R, S, and T have areas of 12, 15, and 3
respectively. Let g(x) = ! f(t)at.
(-4,1)
R
-2
T.
a) At what value of x does g(x) have a point of inflection? Justify your answer.
b) What is the maximum of g(x)? Show the analysis to support your answer.
c) Find lim (2)=6x
4-x
x--2
d) Let h(x) = : Find h'(- 2).
g(x)
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