Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (b)
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Question 01 (b) 

Select all that apply: When we say that is not differentiable at , we mean (a) does not exist. (b) does not exist. (c) . (d) the graph of may have a corner at . (e) the graph of may have a vertical asymptote at . 
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Hint 

A function can be continuous but not differentiable. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Statement (a) is incorrect because a function can be defined at a point without being differentiable there (for example, if the function has a corner at ). Statement (c) says that is discontinuous at , but a function can be continuous at a point without being differentiable there (again, a function with a corner is an example of this). Statement (b) says precisely that is not differentiable at , and statements (d) and (e) are each examples of cases when a function is not differentiable at a point. Answer: The correct answers are . 