Which of the following statements are always correct? (1) If f is not continuous at x=a, then the graph of f has a sharp corner at x=a. (2) If f is not continuous, then f is not differentiable. (3) If f is not differentiable at x-a, then the graph of f has a sharp corner at x=a. O (1) (2) (3) O (1) and (2) O (1) and (3) (2) and (3) all of them

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Which of the following statements are always correct?
(1) If f is not continuous at x=a, then the graph of f has a sharp corner at x=a.
(2) If f is not continuous, then f is not differentiable.
(3) If f is not differentiable at x=a, then the graph of f has a sharp corner at x=a.
O (1)
O (2)
(3)
O (1) and (2)
O (1) and (3)
O (2) and (3)
O all of them
Transcribed Image Text:Which of the following statements are always correct? (1) If f is not continuous at x=a, then the graph of f has a sharp corner at x=a. (2) If f is not continuous, then f is not differentiable. (3) If f is not differentiable at x=a, then the graph of f has a sharp corner at x=a. O (1) O (2) (3) O (1) and (2) O (1) and (3) O (2) and (3) O all of them
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