query: Is $|f'(x)| \le 2\sqrt{\alpha \beta}$?
positive_passages.docid: 134382
positive_passages.text: Proving bounded first derivative
negative_passages.docid: 46844
negative_passages.text: Show that if $\int_0^x f(y)dy \sim Ax^\alpha$ then $f(x)\sim \alpha Ax^{\alpha -1}$
negative_passages.docid: 7042
negative_passages.text: Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
negative_passages.docid: 122485
negative_passages.text: Limit of $f(x+\sqrt x)-f(x)$ as $x \to\infty$ if $|f'(x)|\le 1/x$ for $x>1$
negative_passages.docid: 72892
negative_passages.text: Does $\sqrt{x}$ have a limit for $x \to 0$?
negative_passages.docid: 97583
negative_passages.text: Let $\alpha, \beta, \gamma$ be cardinals, $\beta \leq \gamma$, prove $\alpha ^{\beta}\le \alpha ^{\gamma}$
negative_passages.docid: 158647
negative_passages.text: If $|f(z)|\le |f(z^2)|$ then prove that $f$ is constant
negative_passages.docid: 89429
negative_passages.text: Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
negative_passages.docid: 27072
negative_passages.text: If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
negative_passages.docid: 97454
negative_passages.text: Find the value of $\alpha-\beta$ if $g(x,y)=\alpha x+\beta y$ is a Hahn-Banach extension of $f$
negative_passages.docid: 145173
negative_passages.text: $f: \mathbb{R}^2-\{0\} \rightarrow \mathbb{R}$ is continuously differentiable and $f(\alpha x) = \alpha^2f(x)$, then $x \cdot \nabla f(x) = 2 f(x)$
negative_passages.docid: 21954
negative_passages.text: A question about $f(x)\equiv 0$
negative_passages.docid: 5180
negative_passages.text: How to show $\alpha\int_a^cf(x)dx+\beta \int_c^b f(x)dx =0$ means $f(x)=0$ everywhere $?$
negative_passages.docid: 37489
negative_passages.text: Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
negative_passages.docid: 132431
negative_passages.text: Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
negative_passages.docid: 56391
negative_passages.text: Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
negative_passages.docid: 152105
negative_passages.text: When is $x^{\alpha}\sin(x^{\beta})$ uniformly continuous for $\alpha, \beta > 0$?