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posted by  JC37 on 11/26/2008 10:21:52 AM  |  status: Live  

Derivatives

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  Which statement is true?
  1. If f (x) is continuous at x = a, then f’(a) exists
  2. If f ’ ( c ) = 0, then f has a local maximum or minimum at (c, f (c ))
  3. If f ’’ ( a ) = 0, then f has an inflection point at (a, f(a)).
  4. If f is differentiable at x = c, then f is continuous at x = c.
  5. If f is continuous on (a, b), then f attains a maximum value on (a, b).

 I believe it is #4. I would appreciate if anyone could tell me if I am correct. Thanks. John
Tags: Calculus

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posted by The Joker on 11/26/2008 11:18:14 AM  |  status: Live
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JC37's comment:
"Thanks for the confirmation!"
Response Details:
Yes you are correct number 4 is right. Since If f (x) is continuous at x = a, then f’(a) exists  is not true, x=c is true. :)
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posted by Lord Font le Roy on 11/26/2008 11:29:48 AM  |  status: Live
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JC37's comment:
"Thanks for the explanation!"
Response Details:
Yes, differentiability always implies continuity (statement #4), however, continutiy does not imply differentiability (statement #1).  Take for example the graph of the absolute value function.  It is a continuous function, yet it is not differentiable at x=0.
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