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6. The table below shows the behavior of a function f that is everywhere continuous. We also know that f(2) = 4 and lim f(x) = 0. %3D x→∞ x < 4 positive | f" (x) | negative does not exit x = 4 does not exit x > 4 f'(x) negative positive (a) For what values of x is the function increasing? (b) Does the function have a relative maximum at = 4? Why or why not? (c) Does the function have a point of inflection? Justify your answer. If yes, also provide the x-coordinate of the point of inflection. (d) Can we use Mean Value Theorem and/or Rolle's Theorem to analyze the function on the interval [3, 5]? Justify your answer. (e) Sketch a possible graph of this function.

6. The table below shows the behavior of a function f that is everywhere continuous. We also know that f(2) = 4 and lim f(x) = 0. %3D x→∞ x < 4 positive | f" (x) | negative does not exit x = 4 does not exit x > 4 f'(x) negative positive (a) For what values of x is the function increasing? (b) Does the function have a relative maximum at = 4? Why or why not? (c) Does the function have a point of inflection? Justify your answer. If yes, also provide the x-coordinate of the point of inflection. (d) Can we use Mean Value Theorem and/or Rolle's Theorem to analyze the function on the interval [3, 5]? Justify your answer. (e) Sketch a possible graph of this function.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6. The table below shows the behavior of a function f that is everywhere continuous. We also know that f(2) = 4 and lim f(x) = 0. %3D x→∞ x < 4 positive | f" (x) | negative does not exit x = 4 does not exit x > 4 f'(x) negative positive (a) For what values of x is the function increasing? (b) Does the function have a relative maximum at = 4? Why or why not? (c) Does the function have a point of inflection? Justify your answer. If yes, also provide the x-coordinate of the point of inflection. (d) Can we use Mean Value Theorem and/or Rolle's Theorem to analyze the function on the interval [3, 5]? Justify your answer. (e) Sketch a possible graph of this function.
Transcribed Image Text:6. The table below shows the behavior of a function f that is everywhere continuous. We also know that f(2) = 4 and lim f(x) = 0. %3D x→∞ x < 4 positive | f" (x) | negative does not exit x = 4 does not exit x > 4 f'(x) negative positive (a) For what values of x is the function increasing? (b) Does the function have a relative maximum at = 4? Why or why not? (c) Does the function have a point of inflection? Justify your answer. If yes, also provide the x-coordinate of the point of inflection. (d) Can we use Mean Value Theorem and/or Rolle's Theorem to analyze the function on the interval [3, 5]? Justify your answer. (e) Sketch a possible graph of this function.
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