Hello rahul , i'm sorry for ignoring that point. yes! he is right.
actually maxima/ minima(local or global) means first derivative=0 but first derivative=0 doesn't mean it's minima maxima point , as it may be inflection which is neither maxima or minima.
like in y=x^{3 }, x=0 is stationary point where first derivative is =0 but that point is neither maxima or minima.
so in that way your claim is wrong.
sorry from my side for wrong answer.