The ratio used in the

**The average velocity for the time interval determined by a fixed time and a varying instant for an object moving on a straight line;****The slope of a secant line between a fixed point and a varying point on the graph of the function;****The average rate of change of a variable depending on an independent variable determined by a fixed and a varying value of the independent variable.**

The derivative can be visualized using a tangent line on a graph or a focus point and derivative "vector" on a mapping diagram.

On the mapping diagram the derivative can be visualized using focus
points for the average rates that converge to a single focus point for
the best linear approximating function.

The derivative can also be visualized as a vector on the target of the mapping diagram.

The derivative can also be visualized as a vector on the target of the mapping diagram.