Monotonicity at a Point - Mathematics Stack Exchange
2018年6月19日 · For example, let's discuss the monotonicity of y = x² at x = 0. Using the definitions stated above, it is easy to observe that f(0+h) > f(0) and f(0-h) > f(0) but f'(0) = 0. Could someone please help clear the confusion, and tell what's the real definition for monotonicity at a point and also why the two above methods don't agree with each other?
Set Theory and Monotonicity - Mathematics Stack Exchange
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analysis - How can I prove the monotonicity of a function ...
2012年10月11日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Monotonicity of measures - Mathematics Stack Exchange
Monotonicity of measures. Ask Question Asked 10 years, 11 months ago. Modified 10 years, 11 months ago. ...
real analysis - Monotonicity of function of two variables
2015年3月20日 · I have a function of two variables, which I wish to check for monotonicity in the entire function domain. I cant find any formal definition of increasing or decreasing function for multi variable case. Can anybody please guide? Thanks in advance.
Generalizing monotonicity to 2D - Mathematics Stack Exchange
2013年3月5日 · Monotone functions of a single variable are well defined, they just keep increasing when the variable increases (or decreases). I wonder if this concept has a standard generalization to two dimens...
real analysis - How to prove monotonicity of this function ...
2020年1月26日 · $\begingroup$ You can compute a table where each rows represent the sub part of your expressions (there are 4 parts here) and each column represent the points where each sub part of your expression change sign (would be at 1/a, and 1 here), then you can look at the signs of the subparts on both side of those values and finally get the signs of your overall …
calculus - How to measure monotonicity of a list of values ...
$\begingroup$ I think the approach is fundamentally wrong; monotonicity is not a local property, you will not be able to define a satisfactory index by summing local contributions independently from each other, no mater what property you choose. $\endgroup$
Monotonicity with expectation - Mathematics Stack Exchange
2020年3月12日 · Monotonicity with expectation. Ask Question Asked 4 years, 9 months ago. Modified 1 month ago. Viewed 2k ...
real analysis - Monotonicity of a function in two variables ...
2019年12月16日 · Monotonicity of function of two variables. 0. Change of variables to polar coordinates in a double ...