a)f '(x)=[tex] \frac{2(x-1)-2x+1}{( x-1)^{2} }= \frac{2x-2-2x+1}{( x-1)^{2} }= \frac{-1}{ (x-1)^{2} } [/tex]
b) Stim din teorie ca f '(2)=[tex] \lim_{x \to 2} \frac{f(x)-f(2)}{x-2} [/tex]
f '(2)=[tex] \frac{-1}{ (2-1)^{2} }=-1 [/tex]
c)f '(x)<0
x | 1 +∞
_____ |_____________________
f '(x) | ------------------------------- ⇒ descrescatoare pe (1,∞)
_____ |_______________________
f(x) | scade
