Answer to Question #163875 in Functional Analysis for asaana

Question

Show that f(x)=2/x+1 is indected

Answer 1

$f(x)=\frac{2}{x+1}$

$y'=-\frac{2}{(x+1)^2}$

$y''=\frac{4}{(x+1)^3}$

For $x\isin (-\infin,-1)$ : $y''<0\implies f(x)$ is concave downward.

For $x\isin (-1,\infin)$ : $y''>0\implies f(x)$ is concave upward.