Explanation Given: f ' (x) Is continuous at x = 0 and that x = 0 is a critical point f Let f (x) = x 3 sin ( 1 x ) f '(x) = 3x 2 sin ( 1 x ) + x 3 cos ( 1 x ) (-x -2 ) = x (3 x sin ( 1 x ) This formula is not defined at x = 0 but its limits is since -1 ≤ sinx ≤ - and -1 ≤ cosx ≤ 1 for all x | f '(x)= | x | | 3x sin ( 1 x ) -cos ( 1 x ) ≤ | x | ( | 3x sin ( 1 x ) | + | cos ( 1 x ) | ) ≤ | x | ( | x | +1) Sequence theorem lim x → 0 | f'(x) | = 0 but does

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.3, Problem 69E

To determine

Define f (x) = x3 sin (1x) for x¹0 and f (0) = 0

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Chapter 4.3, Problem 68E

Chapter 4.3, Problem 70E

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Chapter 4 Solutions

CALCULUS (CLOTH)

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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Define f (x) = x 3 sin ( 1 x ) for x¹0 and f (0) = 0

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Define f (x) = x3 sin (1x) for x¹0 and f (0) = 0

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Chapter 4 Solutions