Discovering Derivatives

The following interaction applet allows students to take the first step for discovering what a derivative is. They can focus their discovery on single points or animate the graph to gain a greater understanding of how derivatives can change at different points on a graph. The graph in question can be changed allowing the students to discover on several different graphs.
1. Set your f(x)=sin(x), when does your s value or your slope value change from positive to negative? When is it zero? 2. How is f(x) related to g(x)? Make a conjecture and check your conjecture with several different functions put in for f(x). 3. The blue graph or g(x) graph is said to be the derivative of f(x), from your discoveries in questions one and two. Describe what a derivative is generally, in your own words.