Summary

DescriptionNon-strict minimum.svg	Function ${\displaystyle f(x)=\left\{{\begin{array}{l}x^{2}(1+\sin {\frac {1}{x}}),\;x\neq 0\\0,\;x=0\end{array}}\right.}$, an example of non-strict local minimum (for ${\displaystyle x=0}$), while there is no constant part.
Date	27 September 2007
Source	Own work
Author	pl:Olaf

Script

Created with Gnuplot script:

set terminal svg size 800 500 fixed enhanced  fname 'Times'  fsize 16

set output "Not_strict_minimum.svg"
set autoscale fix
set samples 5000

set xrange [-0.1:0.1]
set yrange [0:0.02]

set grid
set xzeroaxis linetype -1 linewidth 2
set yzeroaxis linetype -1 linewidth 2

plot x**2*(1+sin(1/x)) title '' lw 2

Licensing

I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.