And before I even get into the nitty gritty of it, I really just want to get an intuitive feel for what the second derivative test is telling us. So let me just draw some axes here. So let's say that's my y-axis. 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.