3.4-bo'lim : Funktsiyaning ta'rifi
12. \(f\left( x \right)\) funksiyasi uchun ayirma qismi quyidagicha aniqlanadi:
\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\]\(f\left( x \right) = 4 - 9x\) funksiyasi uchun ayirma qismini hisoblang.
Yechim
Biz bu muammoni qismlarga bo'lib hal qilamiz. Avval \(f\left( {x + h} \right)\) ni hisoblaymiz.
\[f\left( {x + h} \right) = 4 - 9\left( {x + h} \right) = 4 - 9x - 9h\]2-qadam
Endi biz \(f\left( {x + h} \right) - f\left( x \right)\) ni hisoblaymiz va biroz soddalashtiramiz.
\[f\left( {x + h} \right) - f\left( x \right) = 4 - 9x - 9h - \left( {4 - 9x} \right) = 4 - 9x - 9h - 4 + 9x = - 9h\]\(f\left( x \right)\) ni ayirishda qavsdan ehtiyot bo'ling. Biz funktsiyani ayirishimiz kerak va shuning uchun funktsiyani ayirishimiz uchun hamma narsa atrofida qavs kerak.
3-qadam
Endi biz to'liq farq ko'rsatkichini hisoblash orqali muammoni tugatishimiz mumkin.
\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h} = \frac{{ - 9h}}{h} = \require{bbox} \bbox[2pt,border:1px solid black]{{ - 9}}\]