Can someone explain this question to me?

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

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).

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.

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.

To help you understand the question, let's break it down into a few parts.

1. Graph: The question mentions a graph, but we cannot see it directly through text. However, the URL provided seems to indicate that the graph is hosted on the website imgur.com. So, to view the graph, you need to go to imgur.com and append "/FdQCV" to the website's URL.

2. Concave up or down: In calculus, a graph is considered to be "concave up" if it is shaped like a bowl opening upwards and "concave down" if it is shaped like a bowl opening downwards. Determining the concavity of a graph helps us understand its curvature.

3. Intervals to test: The question asks for the intervals to use when testing if the graph is concave up or down. This means that you need to select specific intervals on the graph and analyze the behavior of the graph within those intervals to determine whether it is concave up or down.

Without seeing the graph you mentioned, it is difficult to provide precise intervals, but I can give you some general guidance. To test for concavity, you should choose intervals that capture significant changes in the graph's curvature or direction. These intervals can be identified based on the presence of critical points, inflection points, or other points where the graph's behavior changes.

Once you access the graph at the provided URL, you can visually examine the shape and direction of the curve. Look for regions where the curve appears to change from concave up to concave down or vice versa. These points represent potential intervals where you can test the concavity.

Remember to select intervals that are meaningful and cover the relevant parts of the graph. By analyzing the behavior of the function within these intervals, you can determine whether the graph is concave up or down.