Thread: Drawing a function based on the graph of it's derivative

1. Drawing a function based on the graph of it's derivative

This is really confusing me. I know how to get the general shape. For example, I know that when the derivative is zero, there must be a minimum or maximum in the original function since the slope at that point is zero. But how do I know the position. If the derivative graph at x=2 is 3, what does that tell me about the function? It just tells me the slope, but that position could be anywhere, couldn't it? How can I tell the position?

2. Originally Posted by theowne
This is really confusing me. I know how to get the general shape. For example, I know that when the derivative is zero, there must be a minimum or maximum in the original function since the slope at that point is zero. But how do I know the position. If the derivative graph at x=2 is 3, what does that tell me about the function? It just tells me the slope, but that position could be anywhere, couldn't it? How can I tell the position?
You are correct. Remember that arbitrary constant from indefinite integration? That's what you are running in to. So basically, just sketch things out at some arbitrary height and try to be consistent to that.

-Dan