Graphing the derivative of a graph

[ACLerok]

one of my calc assignments asks me to graph the derivative of a graph which can be seen here: http://www.eden.rutgers.edu/~cjjacob/images/fifth.jpg

i already know that when there's a cusp on the graph, the derivative of that point is at zero and that slope determines how the derivative acts. can anyone enlightnem me and give me tips on how to graph this one's derivative? Thanks.

 

[quantumdude]

Sure, here are some tips:

1. When f(x) is increasing, f'(x)>0. When f(x) is decreasing, f'(x)<0.

2. When f(x) is concave up, f"(x)>0. When f(x) is concave down, f"(x)<0.

3. Zeros in f(x) do not generally correspond to zeros in f'(x). (You'd be surprised at how many students goof that one up).

 

[ACLerok]

Thanks!