Graphing

[TheNextOne]

Sketch the graph of a positive continuous function y = f(x) having all of these properties:
absolute maximum point at (0, 4);
f’(x) > 0 if x= (-infinity, 0) U (2, + infinity)
f’(x) < 0 if x= (0,2)
f’’(x) < 0 if x= (-2,2) U (2,infinty)
f’’(x) > 0 if x= (-infinty,-2)
lim (as x approaches – infinty) f(x)=0
lim (as x approaches + infinty) F(x) -3

This is what I have:
absoulte maximum at (4,0)
f(x) is increasing from (- infinty,0) and then again from (2, positive infinity)
F(x) is decreasing from (0,2)
the critical points are -2,0,2,4
and there are horizontal aymptopes at y= 0 and y=3

I don't think this is right. Can anybody show me how to properly interpret this question.

 

[TheNextOne]

This is what I have:

absoulte maximum at (4,0)
f(x) is increasing from (- infinty,0) and then again from (2, positive infinity)
F(x) is decreasing from (0,2)
the critical points are -2,0,2,4
and there are horizontal aymptopes at y= 0 and y=3
F(x) is concave down from -2 to 2 and from 2 to infinity
f(x) is concave up from - infinity to - 2

Can anybody draw the diagram to verify if i am doing it correctly?