Xe^(-x^2/128) absolute max and absolute min

Extrema can occur when the derivative is zero or undefined.



Maxima occur where the first derivative is zero and the second derivative is negative; minima where the second derivative is positive. You have



At the critical points, you get




So you have a minimum at and a maximum at .

Meanwhile, as , it's clear that , so these extrema are absolute on the function's domain.