Hosila, uning geometrik va fizik ma’nosi
Javoblar ota-onalar va o‘qituvchilar uchun.
1
Ta’rif bo‘yicha f(x) = x² + 4x ning hosilasini toping va f′(3) ni hisoblang.
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2
Nuqta s(t) = 2t³ − t (m) qonun bilan harakatlanadi. (t³)′ = 3t² dan foydalanib, t = 1 s va t = 3 s dagi tezliklarni toping.
v(t) = 6t² − 1; v(1) = 5 m/s, v(3) = 53 m/s.
3
f(x) = 2/x (x ≠ 0) ning hosilasini ta’rif bo‘yicha toping. Hosila ishorasi haqida nima deyish mumkin?
f(x + h) − f(x) = −2h/((x + h)x), demak, f′(x) = −2/x². Hosila doim manfiy.
4
y = x³ grafigiga qaysi nuqtalarda urinma y = 12x − 5 to‘g‘ri chiziqqa parallel? ((x³)′ = 3x².)
3x² = 12 ⇒ x = ±2; nuqtalar (2; 8) va (−2; −8).
5
Suv bakidagi suv hajmi V(t) = 5t² + 20 litr (t — daqiqa, (t²)′ = 2t). t = 4 min dagi hajmning o‘zgarish tezligini va birligini ayting.
V′(t) = 10t, V′(4) = 40 l/min.