T14
Najděte intervaly, na kterých je funkce rostoucí, resp. klesající:
161.
\( f(x) = 2 + x − x^2 \) plot f(x) = 2 + x − x^2
164.
\( f(x) = \frac{\sqrt{x}}{x + 100} \) sqrt x / ( x + 100)
162.
\( f(x) = 3x − x^3 \) plot f(x) = 3x − x^3
163.
\( f(x) = \frac{2x}{1 + x^2} \) f(x) = 2x / (1 + x^2)
165.
\( f(x) = x + \sin x \) f (x) = x + sin x
166.
\( f(x) = x + |sin 2x| \) sin 2x| wa =====167.===== \( f(x) = \cos \frac{\pi}{x} \) [[wa> f(x) = cos pi/x
169.
\( f(x) = x^n e^−x , n > 0, x \gt 0 \) f(x) = x^n e^−x , n > 0, x >= 0
170.
\( f(x) = x^2 − \ln x^2 \) f(x) = x^2 − ln x^2
168.
\( f(x) = \frac{x^2}{2^x} \) f(x) = x^2 / 2^x
