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4.6-bo'lim : Grafik shakli, II qism

1. Quyida funksiya grafigi berilgan. Funktsiya yuqoriga va pastga botiq bo'lgan intervallarni aniqlang.

The graph of a function on \( - 3 \le x \le 8\). Starting below the x-axis at the left the graph rises to a small peak at approximately \(\left( { - 2,1} \right)\), decreases to the origin, then increases to a peak at approximately \(\left( {4,5} \right)\). It then falls steeply, crossing the x-axis near \(x = 6\), down to a valley at approximately \(\left( {7, - 3} \right)\) and then turns back up to approximately \(\left( {8, - 2} \right)\) at the right end.
Yechim

Haqiqatan ham bu muammo uchun juda ko'p narsa yo'q. Grafikdan biz funktsiyani yuqoriga/pastga bo'g'inda osongina ko'rishimiz mumkin, shuning uchun biz qilishimiz kerak bo'lgan narsa botiqlik qayerda o'zgarishini taxmin qilish (va bu haqiqatan ham taxmin bo'ladi, chunki u har doim ham aniq bo'lmaydi) va intervallarni yozing.

\[\require{bbox} \bbox[2pt,border:1px solid black]{{{\mbox{Concave Up : }}\left( { - 1,2} \right)\,\,\,\& \,\,\,\left( {6,\infty } \right)\hspace{0.5in}{\mbox{Concave Down : }}\,\,\left( { - \infty , - 1} \right)\,\,\,\,\& \,\,\,\,\left( {2,6} \right)}}\]

Shunga qaramay, bu intervallarning so'nggi nuqtalari, eng yaxshi holatda, taxminiydir, chunki konkavlik qayerda o'zgarishi har doim ham aniq bo'lmaydi.