A new school year brings an opportunity to extend and expand one's knowledge of core concepts learned in the past. In Advanced Physics, students used the App "Graphicus" to learn how slopes of tangent lines vary for a function y(x). Students then applied this understanding to the concept of the derivative in calculus.
Students entered a function y(x), analagous to x(t) or v(t), and then the students, by moving the trace function along the curve, could determine how the first and second derivative change as a function of time. Students then related this analysis to how the velocity and acceleration of an object would change if the inputted function represented x(t).