Hi,

I was just making sure if I was getting the hang of making a sign chart.

So it's basically critical numbers of the derivative, then you would take this derivative and put it into an x and f(x) sign chart.

After that you would plug in points between critical numbers to find where it ends up positive, and where it ends up negative, thus you'll be able to find the maximum if it goes from negative to positive (With the critical number in between, meaning that is the maximum point), and when it's positive to negative, then it would be a minimum.

For the Concavity,

It would just be Points of Inflections instead of critical numbers (which is similar to critical numbers to the first derivative, since it's the zeroes, but this time it's the zeroes for the second derivative)

So that would mean it's the same thing, use the points of inflections and see whether it concaves up and concaves down?

But just making sure, it's the same way right? From Positive to Negative is Concave Up, and Negative to Positive is Concave down?

Oh wait... isn't it the max and min as well, so I'm not sure whether it means concave up and concave down.

And Increasing would be both positive (as in positive critical number positive), and decreasing would be both negative.

So did I get the sign chart down right?

Just making sure if I got the hang of it. Thanks!