query: Are the endpoints of the domain of a function counted as critical points?
positive_passages.docid: 26542
positive_passages.text: Can critical points occur at endpoints? E.g. $f(x) = \frac{1}{x}$ at the interval $[1,4]$
negative_passages.docid: 8226
negative_passages.text: Proving that a function has a removable singularity at infinity
negative_passages.docid: 148470
negative_passages.text: bound of the function
negative_passages.docid: 4196
negative_passages.text: A valid proof for the invariance of domain theorem?
negative_passages.docid: 58005
negative_passages.text: definition of meromorphic function : it may have removable singularities
negative_passages.docid: 43419
negative_passages.text: At unique critical point, does local max imply global max?
negative_passages.docid: 56712
negative_passages.text: How can I find the domain and derivative of the function?
negative_passages.docid: 141156
negative_passages.text: The domain of $\ln(x)^{\ln(x)}$
negative_passages.docid: 133636
negative_passages.text: Is $\mathbb Z[X]/(X^2-1)$ a domain?
negative_passages.docid: 93694
negative_passages.text: Boundary behaviour of holomorphic function on unit disk
negative_passages.docid: 50104
negative_passages.text: Is there a built-in function which detects singularities in a function?
negative_passages.docid: 77877
negative_passages.text: Is there a domain "larger" than (i.e., a supserset of) the complex number domain?
negative_passages.docid: 35751
negative_passages.text: Is There a Problem with This Professor's Proof Concerning Interior and Boundary Points?
negative_passages.docid: 146613
negative_passages.text: Mathematically, how are the critical t values calculated?
negative_passages.docid: 537
negative_passages.text: Set of branch points isn't discrete, but branch points are isolated?
negative_passages.docid: 15690
negative_passages.text: Is a function defined at a single point continuous?
negative_passages.docid: 129765
negative_passages.text: Mean value theorem for the second derivative, when the first derivative is zero at endpoints