Parametric Curves, Part 13 (The outputs of speed(t) give the slopes of dist(t))

The outputs (values) of the speed function give the slopes of the distance-traveled function. The calculus being developed is approached more from an intuitive, physical, and geometric perspective (like a physics teacher would do) and less from a rigorous mathematical perspective (like a math teacher would do) to make it more accessible to precalculus students. Take time to illustrate these ideas with examples involving graphs, difference quotients, and derivatives. The examples involve h(t) = t^2, h(t) = sqrt(t), and h(t) = 4*(t - 1/2)^3 + 1/2.