query: How prove this inequality $[f(x)]^2+[f'(x)]^2\le \max{(A,B)}$
positive_passages.docid: 20192
positive_passages.text: Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
negative_passages.docid: 57026
negative_passages.text: $f(0)=f'(0)=f'(1)=0$ and $f(1)=1$ implies $\max|f''|\geq 4$
negative_passages.docid: 112676
negative_passages.text: Inequality $(a+b+c)(ab+bc+ca)(a^3+b^3+c^3)\le (a^2+b^2+c^2)^3$
negative_passages.docid: 15232
negative_passages.text: Proving an inequality involving real powers
negative_passages.docid: 139774
negative_passages.text: On the inequality $ \int_{-\infty}^{+\infty}\frac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \le n^{3/2}\pi.$
negative_passages.docid: 90343
negative_passages.text: Proving the inequality $|e^z-1|\leq e^{|z|}-1$
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 40936
negative_passages.text: How prove this integral inequality
negative_passages.docid: 39451
negative_passages.text: Proving inequation with maximum and 2nd derivative
negative_passages.docid: 19078
negative_passages.text: Prove an interpolation inequality
negative_passages.docid: 91617
negative_passages.text: Prove this inequality $a \sqrt{1-b^2}+b\sqrt{1-a^2}\le1 $
negative_passages.docid: 34081
negative_passages.text: Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
negative_passages.docid: 156555
negative_passages.text: Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
negative_passages.docid: 58832
negative_passages.text: How prove this $\int_{a}^{b}[f''(x)]^2dx\ge\dfrac{4}{b-a}$
negative_passages.docid: 61162
negative_passages.text: Show that $\left(\int_0^1 f(x)\,dx\right)^2\leq2\int_0^1x\, f(x)^2\,dx $
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 16418
negative_passages.text: Showing that $\frac{f(x)-f(x-h)}{h} \le f'(x) \le \frac{f(x+h)-f(x)}{h}$ given that f' is increasing