9. Тақырыбы: Функцияны туынды арқылы зерттеу
және оның графигін сызу.
Жоспар:
Функцияның монотондық аралықтарын табу.
Функцияның экстремумдерін табу.
Асимптоталарды табу.
Функция графигін сызу.
Y=f(x) функциясын зерттеу үшін ол функцияның анықталу обылысының кейбір нүктелерінде, кейбір интервалдарында қандай қасиеттерге ие болуын функциянығ туындысы жәрдемінде оңай анықтауға болады екен.
Төменде берілген функцмяны туынды арқылы зерттеп соңында графигін сызамыз
Мысал .y=x+ функциясын зерттеп оның графигін Эскизын сызу керек
Функцияның анықталу обылысын табамыз.
Берілген функция x=0 ден бөлек ох өсіндегі барлық нүктелерде анықталған, x=0 нүктесінде график түзіледі.
Функциянығ жұп –таұтығын анықтау f(-x)=f(x) болса жұп, f (-x)=-f(x) болса тақ функция болады
Y=f (x) =x+ f (-x)=-x+
F (-x)=-f (x) болғандыұтан ол тақ функция екен.
3. ox және oy өстерімен графиктің қиылысу нүктелерін табу
x2+4≠0 болғандықтан график ОХ өсімен қиылыспайды;
ОУ; х 0 (1-пунктке қара), яғни ОУ - өсімен де функция графигі қиылыспайды.
4.Асимптоталарын табу.
Горизонтал асимптотаны табу үшін оны у=кх+в деп аламыз.
K=![](data:image/png;base64,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) ![](data:image/png;base64,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)
Горизонтал асимтота теңдеуі: у=x
Достарыңызбен бөлісу: |