Can someone explain this question to me?

Question

What intervals should I use to test whether or not the graph is concave up or down.

Here is the URL for the graph.

imgur dotcom/FdQCV

Answer 1

There are two intervals where the graph is concave down (parts near the maxima), and one where it is concave up (part near the minimum).

The part of the curve where it looks straight is the transition (d²y/dx²=0).

So if you calculate d²y/dx²=0 near the extrema, it will show definitely concave up (d²y/dx²>0) or concave down (d²y/dx²<0).

Answer 2

I still don't understand :| In the book, they show me a chart with given intervals (For ex. x<-2| -2<x<6| x>6|)

Then sub numbers to find if it its concave or up. But this question doesn't have an equation but graph instead.

Answer 3

When an equation is given, you can find where d²y/dx² changes sign. These points would be the limits of concavity, i.e. where concavity changes from one to the other.

Since you're only given a graph, you can only estimate using the the following:
"The part of the curve where it looks straight is the transition (d²y/dx²=0). "

For example,
I find that the graph is pretty much straight at x=-1.3 and x=2.

So from x=-4 to -1.3, it is concave down.
From x=-1.3 to 2, it is concave up.
Finally, from x=2 to 5.5, the curve is concave down again.

You may want to refine the readings of x on your original diagram.