Задача 79945 Нужно решить задачу 467...
Условие
40
Решение
★
[m]\large f'(x) = 3 - \frac{2}{2\sqrt{x}} = 3 - \frac{1}{\sqrt{x}}[/m]
[m]\large f(1) = 3 \cdot 1 - 2 \sqrt{1} = 3 - 2 \cdot 1 = 3 - 2 = 1[/m]
[m]\large f'(1) = 3 - \frac{1}{\sqrt{1}} = 3 - \frac{1}{1} = 3 - 1 = 2[/m]
[m]\large f(4) = 3 \cdot 4 - 2 \sqrt{4} = 12 - 2 \cdot 2 = 12 - 4 = 8[/m]
[m]\large f'(4) = 3 - \frac{1}{\sqrt{4}} = 3 - \frac{1}{2} = 2,5[/m]
[m]\large f(a^2) = 3 \cdot a^2 - 2 \sqrt{a^2} = 3a^2 - 2a[/m]
[m]\large f'(1) = 3 - \frac{1}{\sqrt{a^2}} = 3 - \frac{1}{a}[/m]