Lets use the letter U as your curve: U One way to imagine the the horizontal tangent is that it's where the curve stops going down (negative slope) and starts

Lets use the letter U as your curve: U One way to imagine the the horizontal tangent is that it's where the curve stops going down (negative slope) and starts going up (positive slope). Well, that is also basically the definition of a local minima, and one of those minima is also the global minima.