Show that $f(x,y)$ is continuous at the origin but not differentiable at the origin
103241
A function that is continuous at the origin but not differentiable there
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable
143491
Show that $f$ is differentiable on $(−1, 1)$.
115635
Differentiability of antiderivative and continuity of derivative
157347
continuity, discontinuity derivative and relation to being derivative but its partials are not continuous
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
147758
Differentiable but not continuously differentiable.
11167
A counterexample of a differentiable function on an interval whose derivative is discontinuous
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
33130
$f$ differentiable except in $1$ point
135199
Looking for a function $f$ that is $n$-differentiable, but $f^{(n)}$ is not continuous
70617
Continuity at a point of characteristic function iff the point is not boundary point
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
50111
non-continuous function satisfies $f(x+y)=f(x)+f(y)$
127114
Differentiability implying continuity