Question

f:(1;+∞)-> R , f(x)=\frac{x+2}{x-1}
f'(x)=-\frac{3}{(x-1)^2}
b) Aratati ca functia f este conveca pe intervalul (1;+∞)

Answer 1

[tex]\text{Mai derivand inca odata se obtine:}\\ f^{''}(x)=\dfrac{6}{(x-1)^3} \ \textgreater \ 0,\forall x\in(1,\infty)\Rightarrow \text{f concava}.[/tex]