For this problem, we have been given the graph of a function. We've been asked to approximate the critical numbers of this function and they were going to classify them minimums, maximums or none. So, first, let's remember what a critical number is. Critical numbers. If I have a function f of X, critical numbers are going to happen in one of two places either where the derivative of the function is zero or the derivative is undefined. So what does that look like when we're looking at a graph and not necessarily the equation of the function? Well, if the derivative is zero, that means I have a slope of zero. Or if you can imagine a tangent line means a tangent line is going to be horizontal. The other option is the derivative is undefined. That often happens where you have a cusp. Maybe it's going down like this, up to a peak. There's something going on where I don't have a defined slope at that point. So let's take a look at the function we have here, We do have a cusp. We do have a case where we have, the derivative is undefined and that happens at the .20. At that point, I do have a cusp. So that's going to give me an undefined derivative. I also have to places where I'm going to have, if I imagine a tangent line, it would be horizontal and that's at the top of those two peaks. One happens when X equals equals one, so that's the 10.13 And then again when X is three, so that's the 30.33 So three points. Now let's classify them first. Let's start with um The Cusp that undefined point at 20. That is the lowest point on our graph. Okay. Nothing is right there on the X axis, there's nothing below that. So this is a minimum point. It is definitely a relative minimum because everything around it is bigger. This is the lowest point locally, but it's also the absolute minimum because nowhere else on the graph, is there any point lower than this one? Okay. How about the blue points? The tops of those peaks? Well, those are maximums and they look like they have. If I'm eyeballing this, they look like they have the same value. So I would say these are both maximums. They are relative maximum, certainly because everything around them, the value, the function is less, but nothing anywhere on this interval has a higher value. So they are also absolute maximums. So three critical points to maximums and one minimum.