Proving $f'$ can't have a jump discontinuity point
32694
Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function.
136714
Proving that $\lim_{x \to 0} \frac{f(x)}{|x|}=1$ implies $f$ is not differentiable at $0$.
132730
Is there an everywhere discontinuous increasing function?
70458
Show that it is possible that the limit $\displaystyle{\lim_{x \rightarrow +\infty} f'(x)} $ does not exist.
134382
Proving bounded first derivative
24449
How discontinuous can a derivative be?
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
20688
Discontinuous functions with closed graphs
18222
Set of continuity points of a real function
41043
example of discontinuous function having direction derivative
83907
$f$ bounded but $f'$ isn't
44607
Prove that a continuous function on a closed interval attains a maximum
27775
Proving a function is not a contraction
154572
Continuity of a function at an isolated point
139763
A function takes every function value twice - proof it is not continuous
127538
Show $f(x)=x\ln x$ is not uniformly continuous
140153
Conjectures Involving floor(x)/piecewise continuity with regards to Integration and Differential Equations