In fourier series, why there should be finite maxima and minima (dirichlet conditions)

why not infinte number of maxima and minima?

Answer 1

[Walter Roberson]

This is not a question about MATLAB. Please use more appropriate resources to investigate fourier theory.

https://www.sciencedirect.com/topics/mathematics/dirichlet-condition

Dirichlet conditions. The function f satisfies the Dirichlet conditions on the interval (–T/2, + T/2) if,(i)

f is bounded on the interval (–T/2, + T/2), and

(ii)

the interval (–T/2, + T/2) may be divided into a finite number of sub-intervals in each of which the derivative f′ exists throughout and does not change sign.

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If you had an infinite number of maxima or minima then you would not be able to satisfy that there are a finite number of sub-intervals in each of which the derivative does not change sign. Each maxima or minima requires a sign change for the derivative.