Secant Lines, Tangent Lines, and Velocity

A ball is launched vertically into the air from the ground with an initial velocity of 96 ft/sec. Its height, h(t) in feet, as a function of time, t in seconds, is given by . Use the sliders for a and b to move points A and B, respectively. The slope of the secant line is given and by adjusting points A and B, we can attempt to estimate the slope of the tangent line at any given point. In the context of the problem, these slopes describe the average velocity of the ball on a given time interval.