Is there a differentiable function whose derivative is greater than or equal to 1 everywhere but 0 at 0?
74810
A function $f$ such that $f' = 0$ when $x < 0$ and $f' = 1$ when $x \geq 0$?
24449
How discontinuous can a derivative be?
87743
Is a function whose derivative vanishes at rationals constant?
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
31051
Is $f(x,y)=(xy)^{2/3}$ differentiable at $(0,0)$?
150968
Differentiable function has measurable derivative?
122003
From the limit definition of differentiability, determine where the function $f(x) = \sqrt{x}$ is differentiable?
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
155871
Is it possible for a function to be smooth everywhere, analytic nowhere, yet Taylor series at any point converges in a nonzero radius?
99795
Derivative of piece-wise function given by $x\sin\frac1x$ at $x=0$
25482
If a function is continuous and differentiable everywhere is the derivative continuous?
26955
Continuous at exactly two points and differentiable at exactly one of them
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
48464
If the derivative approaches zero then the limit exists
128719
Are constants the only continuous functions with "symmetric derivative" zero?