3.5-bo'lim : Trig funksiyalarining hosilalari
11. \(x = \pi \) da \(f\left( x \right) = \tan \left( x \right) + 9\cos \left( x \right)\) ga teguvchi chiziqni toping.
Yechim
Biz bilamizki, funktsiyaning hosilasi bizga teginish chizig'ining qiyaligini beradi, shuning uchun bizga funktsiyaning hosilasi kerak bo'ladi.
\[f'\left( x \right) = {\sec ^2}\left( x \right) - 9\sin \left( x \right)\]2-qadam
Endi biz qilishimiz kerak bo'lgan narsa bu funktsiyani va ko'rib chiqilayotgan nuqtadagi hosilani baholashdir.
\[f\left( \pi \right) = \tan \left( \pi \right) + 9\cos \left( \pi \right) = - 9\hspace{0.5in}f'\left( \pi \right) = {\sec ^2}\left( \pi \right) - 9\sin \left( \pi \right) = 1\]3-qadam
Endi biz qilishimiz kerak bo'lgan narsa teginish chizig'ining tenglamasini yozishdir.
\[y = f\left( \pi \right) + f'\left( \pi \right)\left( {x - \pi } \right) = - 9 + \left( 1 \right)\left( {x - \pi } \right)\hspace{0.25in} \to \hspace{0.25in}\,\require{bbox} \bbox[2pt,border:1px solid black]{{y = x - \pi - 9}}\]Javobda \(\pi \) borligidan hayajonlanmang. Bu shunchaki 9 ga o'xshash raqam va shuning uchun tashvishlanadigan hech narsa yo'q.