How do I figure out the answer to this question?

[lasvegas666]

 

[fresh_42]

What do you think and why?

 

[R.M.]

Start with your three criteria for continuous.

 

[Dr.Peterson]

How do I figure out the answer to this question?

Focus on the region near x=1:

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• Does the graph look continuous there? Why or why not? What does a continuous function look like? What features would disqualify it?
• Does the graph look differentiable there? Why or why not? What does a differentiable function look like?

Each choice is a different combination of the yes/no answers to those two questions.

If you don't know how to answer those questions, then look (in your textbook or elsewhere) for the definitions or examples.

 

[Steven G]

There is a theorem which states that if a function is differentiable at x=a, then the function is continuous at x=a. This theorem will rule out at least one of the choices. Which one(s)?