f(x)=[tex] \frac{3x}{ x^{2} +1} [/tex]
f derivat (x)=[tex] \frac{3( x^{2} +1)-3x*2x}{ ( x^{2} +1)^{2} }= \\ = \frac{3 x^{2} +3-6 x^{2} }{ ( x^{2} +1)^{2} }= \\ = \frac{-3 x^{2} +3}{ ( x^{2} +1)^{2} }= [/tex]
f derivat (x)=0⇒-3x²+3=0⇒-3x²=-3⇒x²=1⇒x₁,₂=+/- 1
x | -∞ -1 1 +∞
________|_____________________
f derivat (x)|---------0 +++++ 0----------- ⇒ f strict descrescatoare pe (-∞,-1]
________|_____________________ si pe [1.+∞)
f(x) | scade creste scade f strict crescatoare pe [-1,1]
