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.
(d) the graph of may have a corner at .
(e) the graph of may have a vertical asymptote at .
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A function can be continuous but not differentiable.
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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 .