Determine if the following statements are true or false. If the statement is true, write true and explain why. If there is a theorem, refer to it. If the statement is false, write "false" and give an example that disproves the statement. a. If f(x) is continuous at x=1, then f'(1) exists. b. If f'(1) exists, then f(x) is continuous at x=1

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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Determine if the following statements are true or false. If the statement is true, write true and explain why. If there is a theorem, refer to it. If the statement is false, write "false" and give an example that disproves the statement.

a. If f(x) is continuous at x=1, then f'(1) exists.

b. If f'(1) exists, then f(x) is continuous at x=1

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