Funksiyaning o‘sishi va kamayishi
Javoblar ota-onalar va o‘qituvchilar uchun.
1
6^(−1/2) va 9^(−1/2) ni taqqoslang.
6^(−1/2) > 9^(−1/2), chunki r < 0 va 6 < 9
2
x^(2/3) = 9 tenglamani yeching (x > 0).
27
3
x⁻² = 1/16 tenglamaning musbat ildizini toping.
4
4
y = x^(1/4), y = x^(−1/4), y = x⁵ funksiyalardan qaysilari x > 0 da kamayadi?
faqat y = x^(−1/4)
5
y = x − 1/x funksiya x > 0 da o‘sishini isbotlang.
x₁ > x₂ > 0 da y(x₁) − y(x₂) = (x₁ − x₂) + (x₁ − x₂)/(x₁x₂) = (x₁ − x₂)(1 + 1/(x₁x₂)) > 0.