f (x) = x^2 - 2x + 1 funksiyasini ko'rib chiqing, bu parabolik egri chiziqni yuqoriga ochadi. Biz ushbu funksiyaning minimal qiymatini topmoqchimiz. Buni amalga oshirish uchun, f (x) ning x ga nisbatan hosilasini topish orqali kalkuldan foydalanishimiz mumkin: f' (x) = 2x - 2 f' (x) ni nolga teng qilib, x uchun yechim topamiz: 2x - 2 = 0 x = 1 f (x) ning kritik nuqtasi x = 1. Bu minimal yoki maksimal ekanligini aniqlash uchun, biz f (x) ning ikkinchi hosilasini olishimiz mumkin: f' (x) = 2 f' (x) barcha x uchun musbat bo'lgani uchun, biz x = 1 kritik nuqtasi f (x) ning minimal qiymatiga mos kelishini bilamiz. Biroq, kosmik matematik hazil shundaki
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