What is the relationship in the graphs between the original ...

[Hawke]

What is the relationship in the graphs between the original function, the derivative, and the 2nd derivative?

I have a math final and can't find any quick points that outline the ideas.
I know that a min or max on the original function is a zero on the derivative.
When the concavity changes on the original function, what does it mean on the 2nd derivative?

Thanks so much!

[ricki]

You probably already know this, but the second derivative is just the slope if the derivative. So if you have a graph, say a parabola and take the derivative you can find the exact point where the max or min occurs by finding when the slope is zero, as you mentioned.
Assuming this is in two dimensions, the second derivative will tell you the slope of the first derivative and so if this is negative at points just before the concave point, and positive after you will know the derivative function falls downward(has negative slope) and then rises again after the point, and so the original function curves downward then rises again and so the point must be a minimum.