Let's say this is my x-axis. And let's say I have a function that has a relative maximum value at x equals c. So let's say we have a situation that looks something like that, and x equals c is right over, so that's the point c, f of c. So, I can draw a straighter dotted line. So that is x being equal to c. And we visually see that we have a local maximum point there, and we can use our calculus tools to think about what's going on there. Well, one thing that we know, we know that the slope of the tangent line, at least the way I've drawn it right over here, is equal to zero. So we can say f prime of c is equal to zero. And the other thing we can see is that we are concave downward in the neighborhood around x equals c. So notice our slope is constantly decreasing. And since our slope is, notice it's positive, it's less positive, even less positive, it goes to zero, then it becomes negative, more negative, and even more negative.