Science:Math Exam Resources/Courses/MATH110/April 2018/Question 01 (b)/Solution 1

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 ${\textstyle x=2}$). Statement (c) says that ${\textstyle f}$ is discontinuous at ${\textstyle x=2}$, 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 ${\textstyle f}$ is not differentiable at ${\textstyle x=2}$, and statements (d) and (e) are each examples of cases when a function is not differentiable at a point.

Answer: The correct answers are ${\textstyle {\color {blue}(b),(d),(e)}}$.