Show that $\max_{x\in[a,b]}|f'(x)|\geq\frac{4}{(b-a)^2}\int_a^b|f(x)|dx$
34081
Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
154247
Proving $f(x)$ attains $\max$ or $\min$ when $f(x)\to0$ as $|x|\to\infty$.
78174
How prove this inequality $\left(\int_{0}^{1}f(x)dx\right)^2\le\frac{1}{12}\int_{0}^{1}|f'(x)|^2dx$
16634
How to show $\lim_{n \to \infty} \sqrt[n]{a^n+b^n}=\max \{a,b\}$?
44653
$(\int f_1d\mu)^2+\cdots+(\int f_nd\mu)^2\leq(\int \sqrt{f_1^2+\cdots+f_n^2}d\mu)^2$
85535
Finding maximum of $|f'(i)|$
44607
Prove that a continuous function on a closed interval attains a maximum
157328
A complex analysis problem to prove an inequality
155415
Minimax problem for optimization $\inf \sup \frac{x f(x)}{\int_0^1 f(t) dt}$
18261
Prove $\int_{a}^{b}{f(x)dx}>0$.
64844
Finding $E(|X_1|\ |\max |X_i| )$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
105768
Proof involving absolute value and maximums
156599
Wirtinger Inequality: $\int_0^1 f'^2 \geq \pi^2 \int_0^1 f^2 $
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
75653
Prove that $|f ''|\ge 4$