Snowboarding over Derivatives
This Demonstration shows the geometric nature of the first and second derivative using a snowboarder. Imagine watching a snowboarder using a telescope. The inclination of the snowboard gives a numeric value for the first derivative, as read from the calibrated scale on the edge of the telescope. Here we assume that the snowboarder is not jumping, so that the board is always tangent to the slope. The second derivative is represented geometrically by how the front tip of the snowboard rotates upwards or backwards. You can make flags show in places where the first/second derivative are zero and you can choose different courses for practice. The author has found this Demonstration useful with his students, explaining using one course and letting them try to determine sign diagrams for the other courses.