Typical applications of evolutionary optimization involve the off-line approximation of extrema of static multi-modal functions. Methods which use a variety of techniques to self-adapt mutation parameters have been shown to be more successful than methods which do not use self-adaptation. For dynamic functions, the interest is not to obtain the extrema but to follow it as closely as possible. This paper compares the on-line extrema tracking performance of an evolutionary program without self-adaptation against an evolutionary program using a self-adaptive Gaussian update rule over a number of dynamics applied to a simple static function. The experiments demonstrate that for some dynamic functions, self-adaptation is effective while for others it is detrimental.