# Sketching the graph of a function

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 $-1<x<3$

$\displaystyle \lim _{x\to \infty}$ $f(x)=-3$.

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It should be in the shape of a bell. – Joel Cohen Mar 19 '13 at 22:02
Note: the task is to sketch a graph. (It's not unique.) Which of the criteria are you having trouble with? – Sammy Black Mar 19 '13 at 22:02
The derivative are kind of confusing me and the conditions a bit.. – Fernando Martinez Mar 19 '13 at 22:07
Think about what it means for a function's first and second derivatives to be zero at certain points. You may find this and this article helpful. – Nik Bougalis Mar 20 '13 at 0:12
@nikbougalis with those helpful website I think I understand how to graph to betterthanks – Fernando Martinez Mar 20 '13 at 21:03