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Is it necessary for some point ##x## of the function to be saddle that
##f'(x)=0##?
##f'(x)=0##?
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What you have written isn't clear. For one thing, saddle points aren't applicable to functions of a single variable. For another, do you mean that f'(x) = 0 for some specific value of x? Or do you mean that f'(x) is identically equal to zero?Is it necessary for some point of the function to be saddle that
##f'(x)=0##?
Yes. Let f(x) = x^{1/3}.Yes I mean for particular value of ##x##. For some ##x_0## is it possible situation that
##f'(x_0)\neq 0## and that in ##x_0## function has inflection point?