# Changes

## Sinc function

, 17:43, 19 December 2011
Key data
| [[local maximum value]]s and points of attainment || The local maxima occur at points $x$ satisfying $\tan x = x$ and $x \in [2n\pi,(2n + 1)\pi]$ or $x \in [-(2n + 1)\pi,-2n\pi]$ for $n$ a positive integer.<br> There is an anomalous local maximum at $x = 0$ with value 1. Apart from that, the other local maxima occur at points of the form $\pm(2n\pi + \alpha_n)$ where $\alpha_n$ is fairly close to $\pi/2$ for all $n > 0$. The local maximum value at this point is slightly more than $1/(2n\pi + \pi/2)$.
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| [[local minimum value]]s and points of attainment || The local minima occur at points $x$ satisfying $\tan x = -x$ and $x \in [(2n - 1)\pi,2n\pi]$ or $x \in [-2n\pi,-(2n - 1)\pi]$ for $n$ a positive integer.<br> The local minima occur at points of the form $\pm(2n\pi - \alpha_n)$ where $\alpha_n$ is fairly close to $\pi/2$ for all $n > 0$. The local minimum value at this point is slightly less than $-1/(2n\pi - \pi/2)$.
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| [[point of inflection|points of inflection]] || {{fillin}}
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