T16
Vyšetřete konvexnost, resp. konkávnost, funkcí:
190.
\( f(x) = 3x^2 − x^3 \) plot f(x) = 3x^2 − x^3
194.
\( f(x) = x + \sin x \) f(x) = x + sin x
191.
\( f(x) = \frac{a^3}{a^2 + x^2} a > 0 \) [wa> f(x) = a^3/(a^2 + x^2) a > 0 ]]
192.
\( f(x) = x + \sqrt[3]{x^5} \) f(x) = x + cuberoot x^5
193.
\( f(x) = \sqrt{1 + x^2} \) f(x) = sqrt(1 + x^2)
195.
\( f(x) = e^−x^2 \) plot f(x) = e^−x^2
196.
\( f(x) = \ln(1 + x^2 ) \) f(x) = ln(1 + x^2 )
197.
\( f(x) = x \sin \ln x \) plot f(x) = x sin ln x
198.
\( f(x) = x^x , x>0 \) f(x) = x^x , x>0
