Extrema and first variation



My physics book states:

An extremum can be characterised as the place where the first variation of
the function vanishes.
"followed by this equation"

delta f = sum from a=1 to n [(partial delta f / partial delta x superscript
a) delta x superscript a] = 0

Sorry about the text.
What does this mean?
I'm not sure why a summation has appeared in here
Zinc
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Relevant Pages

  • Re: Extrema and first variation
    ... An extremum can be characterised as the place where the first variation of the function vanishes. ... delta x superscript a] = 0 ... x to x + delta x is approximately ...
    (sci.math)
  • Re: Extrema and first variation
    ... Zinc Potterman wrote: ... delta x (that latter part is the sum of partial derivatives times changes in x). ... If f has an extremum at x, this change must be zero, ...
    (sci.math)