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. 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
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)
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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