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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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Please answer the attached question and explain in detail how you arrived at the answers. Thank you. 

C X f(x) f'(x) f"(x) 0 -1 4 0<x< 1 Negative Positive 1 0 0 -2 Negative 0 1<x<2 Positive Positive Positive a) For 0<x< 4, find all values of x at which fhas a relative extremum. Determine whether fhas a relative maximum or a relative minimum at each of these values. Justify your answer. 2 c) Let g be the function defined by c) Let g be the function defined by g(x)=f(t)dt 2 DNE 2<x<3 Positive 3 0 Negative -3 DNE Negative 0 3<x< 4 Negative Negative 2. Let f be a function that is continuous on the interval [0, 4). The function fis twice differentiable except at x = 2. The function fand its derivatives have the properties indicated in the table above, where DNE indicates that the derivatives of f do not exist at x = 2. Positive g(x)= [f(t)dt on the open interval (0,4) For 0<x< 4, find all values of x at which g has a relative extremum. Determine whether g has a relative maximum or a relative minimum at each of these values. Justify your answer. d) For the function g defined in part (c), find all values of x, for 0<x<4, at which the graph of g has a point of inflection. Justify your answer.
Transcribed Image Text:C X f(x) f'(x) f"(x) 0 -1 4 0<x< 1 Negative Positive 1 0 0 -2 Negative 0 1<x<2 Positive Positive Positive a) For 0<x< 4, find all values of x at which fhas a relative extremum. Determine whether fhas a relative maximum or a relative minimum at each of these values. Justify your answer. 2 c) Let g be the function defined by c) Let g be the function defined by g(x)=f(t)dt 2 DNE 2<x<3 Positive 3 0 Negative -3 DNE Negative 0 3<x< 4 Negative Negative 2. Let f be a function that is continuous on the interval [0, 4). The function fis twice differentiable except at x = 2. The function fand its derivatives have the properties indicated in the table above, where DNE indicates that the derivatives of f do not exist at x = 2. Positive g(x)= [f(t)dt on the open interval (0,4) For 0<x< 4, find all values of x at which g has a relative extremum. Determine whether g has a relative maximum or a relative minimum at each of these values. Justify your answer. d) For the function g defined in part (c), find all values of x, for 0<x<4, at which the graph of g has a point of inflection. Justify your answer.
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