How Do the Graphs of y, y', and y'' Relate to Anti-Derivatives?

[Miike012]

Homework Statement

Say y = x^3

Then: y' = 3x^2
y'' = 6x


My question is... Let's say I graphed y y' and y''. Do these graphs give us any info about the anti derived graph?

For instance just by looking at the y' graph can I gather up any info for y graph?

 

[Char. Limit]

Yep. Where y' is 0, the slope is zero and the graph has a critical point. Where y'>0, you know the graph is going up. Where y'<0, you know the graph is going down.

This is all covered in curve sketching.