query: Bound on first derivative $\max \left(\frac{|f'(x)|^2}{f(x)} \right) \le 2 \max |f''(x)|$
positive_passages.docid: 107894
positive_passages.text: Inequality involving the sup of a function and its first and second derivatives
negative_passages.docid: 51107
negative_passages.text: Limit distribution of $\frac1n\cdot \max(X_1,X_2,...,X_n)$ for $(X_n)$ i.i.d. standard Cauchy
negative_passages.docid: 75548
negative_passages.text: second derivative of the inverse function
negative_passages.docid: 154223
negative_passages.text: Find the maximum value of $ f(x) = \int^{x}_{0} \sqrt{(x^2-x)^2+y^4}~dy$
negative_passages.docid: 97558
negative_passages.text: Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
negative_passages.docid: 118884
negative_passages.text: The sine inequality $\frac2\pi x \le \sin x \le x$ for $0<x<\frac\pi2$
negative_passages.docid: 53748
negative_passages.text: Find maximum value of $\int_{0}^{1}\left(f(x)\right)^3dx$
negative_passages.docid: 95626
negative_passages.text: $\int_X |f_n - f| \,dm \leq \frac{1}{n^2}$ for all $n \geq 1$ $\implies$ $f_n \rightarrow f$ a.e.
negative_passages.docid: 34398
negative_passages.text: Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 54321
negative_passages.text: Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
negative_passages.docid: 93806
negative_passages.text: $\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
negative_passages.docid: 100608
negative_passages.text: Prove that $\|v\|_{H^1(\Omega )}\leq C(\|f\|_{L^2(\Omega )}+\|v\|_{H^{1/2}(\partial \Omega )}+\|\partial _\nu v\|_{H^{1/2}(\partial \Omega )}))$
negative_passages.docid: 104263
negative_passages.text: How to show that $f'(x)<2f(x)$
negative_passages.docid: 131444
negative_passages.text: Local maximum implies derivative is $0$
negative_passages.docid: 127390
negative_passages.text: Second derivative of a composite function
negative_passages.docid: 58629
negative_passages.text: Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.