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. So we know that f prime prime, we know that f prime prime of c is less than zero. And so, I haven't done any deep mathematical proof here, but if I have a critical point where f prime, where our critical point at x equals c, so f prime of c is equal to zero, and we also see that the second derivative there is less than zero, well, intuitively, this makes sense that we are at a maximum value. And we could go the other way. If we are at a local minimum point at x equals c, or relative minimum point, so our first derivative should still be equal to zero, because our slope of a tangent line right over there is still zero, so f prime of c is equal to zero. But in this second situation, we are concave upwards. The slope is constantly increasing.