It might help to think of a specific curve. An example would be a simple parabola: f(x) = x^2. At the bottom of the curve (x = 0), the slope (aka tangent, aka

It might help to think of a specific curve. An example would be a simple parabola: f(x) = x^2. At the bottom of the curve (x = 0), the slope (aka tangent, aka derivative) is 0, or a horizontal line.