If function $f$ has zero value and positive derivative at both endpoints, then $f''(\eta)=f(\eta)$ for some $\eta$
101778
Show that there is $\eta\in(0,1)$ with $f''(\eta)=f(\eta)$
12556
A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
143874
Limit of derivative is zero. Does it imply a limit for f(x)?
108329
If $T\alpha=c\alpha$, then there is a non-zero linear functional $f$ on $V$ such that $T^{t}f=cf$
13150
If the derivative of $f$ is never zero, then $f$ is one-to-one
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
8854
Prove $f $ is identically zero if $f(0)=0$ and $|f'(x)|\le|f(x)|$
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
35264
Must a monotone function have a monotone derivative?
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
25467
Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
114826
Zero Partials imply Constant Function Theorem or Proof
117338
Counterexample to second derivative test when f''(x) is not continuously differentiable