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This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x²) + 3 . (a) Find f'(x) = X - 2x 1 + x 4 (b) Find the critical point of f(x).

This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x²) + 3 . (a) Find f'(x) = X - 2x 1 + x 4 (b) Find the critical point of f(x).

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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This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x²) + 3. (a) Find f'(x) X = = (c) Find f"(x) (b) Find the critical point of f(x). 2x 1 + x = 4 (d) Use the Second Derivative Test to classify the critical point of f. f" (c.p.) = This means that f is ---Select--- ✓at the critical point because f" (c.p.) is ---Select--- We conclude that the critical point is [---Select--- of f.
Transcribed Image Text:This problem illustrates the Second Derivative Test. Let f(x) = - arctan(x²) + 3. (a) Find f'(x) X = = (c) Find f"(x) (b) Find the critical point of f(x). 2x 1 + x = 4 (d) Use the Second Derivative Test to classify the critical point of f. f" (c.p.) = This means that f is ---Select--- ✓at the critical point because f" (c.p.) is ---Select--- We conclude that the critical point is [---Select--- of f.
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