# AP Calculus Unit 2.1 Rates of Change

Topic:
Calculus
Construction used in AP Daily video Unit 2.1 (2020-21 academic year), intended to show how:
1. "average rate of change" may be interpreted as the slope of a secant line over an interval
2. "instantaneous rate of change" (a.k.a. derivative) may be interpreted as the slope of a tangent line at a single input value
3. instantaneous rate of change is the limit of the average rate of change as the width of the interval shrinks to zero.
To change the interval width, drag its right edge left/right. To change the location of the tangent line, drag the blue point of tangency within the interval. This parabola may model the height of an object launched from the ground (height = 0 ft) into the air near the surface of the Earth with constant gravitational acceleration of -32 ft/s/s at an initial velocity of 160 ft/s, assuming no forces acting upon it other than gravity. A more general version of this construction is here, allowing user entry of f(x) equation and dragging of either side of the interval.