how to find breakpoints of a signal based on the frequency of the signal
The samples in the 'f' vector in the Matlab Example 1 code are arbitrary, ...just an example of a lowpass filter. The purpose of that code is to merely show you how the "designed" (actual) freq response is similar to, but not equal to, the "ideal" rectangular  freq response.

I don't like that Matlab Example 1 example. It's confusing to some beginners to have two different magnitude ('m') sample values associated with a single 'f' value of 0.6. A better example would define 'f' as f = [0 0.6 0.7 1].

In any case, the Example 1 example's f = [0 0.6 0.6 1] and m = [1 1 0 0], vectors specify that the lowpass filter's "ideal" passband gain is one at $0*f_s/2$ Hz and is one at $0.6*f_s/2$ Hz. (The '*' symbol means multiply.) So the "ideal" lowpass passband extends from $0*f_s/2$ -to- $0.6*f_s/2$ Hz. The code also specifies that the lowpass filter's "ideal" stopband gain is zero at $0.6*f_s/2$ Hz and is zero at $1*f_s/2$ Hz. So the "ideal" stopband extends from $0.6*f_s/2$ -to- $1*f_s/2$ Hz.

Now if you wanted the filter's "ideal" lowpass passband to extend from $0*f_s/2$ -to- $0.5*f_s/2$ Hz (zero Hz –to- $f_s/4$ Hz), you would define vector 'f' as f = [0 0.5 0.5 1].