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Consider the function f(x) and its derivatives:

Consider the function f(x) and its derivatives:

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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Consider the function f(x) and its derivatives: 1-x² (x² + 1)² 2x(x²-3) (x²+1)3 (a) [] Find the critical numbers of f(x) and show your work to justify. (b) Find the open interval(s) where f is decreasing and the open interval(s) where fis increasing. Show your work to justify your answer. Find the x-coordinate(s) of all local minima of f, and all local maxima of f. Show your work (c) to justify. f'(x) = (e) and f"(x) = (d) Find the open intervals where f is concave up and the open intervals where fis concave down. Show your work to justify. Find the x-coordinates of all inflection point(s) of f, and show your work to justify.
Transcribed Image Text:Consider the function f(x) and its derivatives: 1-x² (x² + 1)² 2x(x²-3) (x²+1)3 (a) [] Find the critical numbers of f(x) and show your work to justify. (b) Find the open interval(s) where f is decreasing and the open interval(s) where fis increasing. Show your work to justify your answer. Find the x-coordinate(s) of all local minima of f, and all local maxima of f. Show your work (c) to justify. f'(x) = (e) and f"(x) = (d) Find the open intervals where f is concave up and the open intervals where fis concave down. Show your work to justify. Find the x-coordinates of all inflection point(s) of f, and show your work to justify.
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