Taking the derivative:
2lnx+2, 2(lnx+1).
Extrema occur at y'=0.
2(lnx+1)=0,lnx=-1
x=e^(-1)=1/e
y=-2/e
So the extrema occurs at (1/e,-2/e)
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when there are extreme values in the data
Generally not without further reason. Extreme values are often called outliers. Eliminating unusually high values will lower the standard deviation. You may want to calculate standard deviations with and without the extreme values to identify their impact on calculations. See related link for additional discussion.
the variance
what do we call a measure that is relatively unaffected by extreme observations
Because it is easily influenced by extreme values (i.e. it is not unbiased).