query: Given a certain differentiable inequality of f show that $a\geq\pi$
positive_passages.docid: 145424
positive_passages.text: If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.
negative_passages.docid: 158180
negative_passages.text: An inequality of $\int_0^1 |f(x)|dx$
negative_passages.docid: 20192
negative_passages.text: Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
negative_passages.docid: 149764
negative_passages.text: If $f$ s twice differentiable and satisfies the following constraints, prove $f'(0)>-\sqrt 2$
negative_passages.docid: 118613
negative_passages.text: Proving an inequality: $|1-e^{i\theta}|\le|\theta|$
negative_passages.docid: 80650
negative_passages.text: Complex differentiability of $f(z)=|z|$
negative_passages.docid: 157328
negative_passages.text: A complex analysis problem to prove an inequality
negative_passages.docid: 98002
negative_passages.text: Let $x$ be a positive real number. Inequality problem with $\pi$ and $x$ terms.
negative_passages.docid: 34081
negative_passages.text: Prove that $|f''(\xi)|\geqslant\frac{4|f(a)-f(b)|}{(b-a)^2}$
negative_passages.docid: 75653
negative_passages.text: Prove that $|f ''|\ge 4$
negative_passages.docid: 7825
negative_passages.text: If $f$ is a concave function and $f(0) \geq 0$ then $f(a+b) \leq f(a) + f(b)$ for all $a,b >0$
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: 137527
negative_passages.text: if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
negative_passages.docid: 15727
negative_passages.text: show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
negative_passages.docid: 15441
negative_passages.text: Show $\frac{1}{4}\leq \mu(A\cap B \cap C)$
negative_passages.docid: 44233
negative_passages.text: How to prove this inequality $ x + \frac{1}{x} \geq 2 $
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 $