Examine the relationship between the first and second derivative and shape of a function.

• Examine the relationship between the first and second derivative and shape of a function

The students will move a point on a given function and observe the sign of the first and second derivative as well as a description of the graph (increasing, decreasing, concave up, concave down). From their observations, students will make conjectures about the shape of the graph based on the signs of the first and second derivative.