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The correct property is: ${\displaystyle \partial ^{2}f(x)/\partial x_{i}^{2}<0}$. This is equivalent to saying

1. the first derivative of the function is decreasing in ${\displaystyle x_{i}}$
2. the second derivative of the function is negative

It seems that people think that it is equivalent to saying "the second derivative of the function is decreasing in ${\displaystyle x_{i}}$". However, this is a statement about the third derivative of ${\displaystyle f}$, and thus it is unrelated to property 4. Thefroyo ( talk) 19:04, 2 October 2013 (UTC) reply

Is it possible to give an example? A concrete function equation and/or plot? E.g. cobb-douglas-style. thanks -- WissensDürster ( talk) 07:35, 5 August 2015 (UTC) reply

Added Cobb-Douglas plot. 195.83.197.185 ( talk) 10:20, 4 November 2022 (UTC) reply

Don't utility functions also necessarily satisfy Inada conditions? AllGloryToTheHypnotoad ( talk) 14:27, 18 August 2017 (UTC) reply

Yup, added. Utility functions satisfying Inada conditions also are necessary for an Euler equation for consumption to be well-defined (we have consumption at the denominator, so we need ${\displaystyle c(t)\neq 0\;\forall \;t\in \mathbb {R} _{+}}$ and Inada conditions make sure this happens by having infinite marginal utility at 0), but since this is already very technical I'm not sure how much it would add to specify this. 195.83.197.185 ( talk) 10:22, 4 November 2022 (UTC) reply