How would I sketch the graph of the following function.
Sketch the graph of a function satisfying the following conditions
$f(1)=2$
$f(-1)=f(3)=-1$
$f'(1)=0$
$f'(x)>0$ for all $x<1$
$f'(x)<0$ for all $x>1$
$f''(-1)=f''(3)=0$
$f''(x)>0$ for all $x<-1$ and for all $x>3$
$f''(x)<0$ for all $-1<x<3$
$\displaystyle \lim _{x\to \infty}$ $f(x)=-3$.