Bounding $|f'|$ given a bound for $|f|$ and $|f''|$.
107894
Inequality involving the sup of a function and its first and second derivatives
48275
$f$ defined $|f(x) - f(y)| \leq |x - y|^{1+ \alpha}$ Prove that $f$ is a constant.
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
76209
Inequalities for combinations of $\int f $ and $\int (1/f)$ where $m\le f\le M$ on an interval
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
134382
Proving bounded first derivative
99644
Finding an Upper Bound on This Inequality
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
111186
Proving that if $|f''(x)| \le A$ then $|f'(x)| \le A/2$
85739
Show that $f(x) = 0$ for all $x \in [a,b]$ given $|f'(x)| \leq C|f(x)| $
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
82745
Showing Entire Function is Bounded
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$
95626
$\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
99927
The closure of $\{ z:|f(z)|<c\}$ is the set $\{z:|f(z)|\leq c\}$.
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$