Prove that $|f'(x)|\leq\sqrt{2MM''}$
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
22294
Maximum and minimum value of $\int_0^1 f(x)dx $ given $|f'(x)|<2$
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
150502
If $f(0) = 0$ and $|f'(x)|\leq |f(x)|$ for all $x\in\mathbb{R}$ then $f\equiv 0$
57026
$f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
28949
Prove $f(x) = 0 $for all $x \in [0, \infty)$ when $|f'(x)| \leq |f(x)|$
118613
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
56958
bounding a $C^1$ function that upholds $f'(t)\leq 1-f(t)^2$
69008
$f'(x) = [f(x)]^{2}$. Prove $f(x) = 0 $
104263
How to show that $f'(x)<2f(x)$
32063
if $f'(x)\rightarrow L$ as $ x \rightarrow \infty$, $-\infty \leq L \leq \infty $ then $ f(x)/x \rightarrow L $ as $x \rightarrow \infty$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
5430
Using Cauchy's integral theorem to prove a inequality
111470
Proof of differentiability of $f(x)$
126165
Prove $|\arctan x - \arctan y|\leq |x-y|$
128495
Integral Inequality $|f''(x)/f(x)|$