Derivative intuition

The  exercise appears under the Differential calculus Math Mission. This exercise uses a function and a graph to explore how the graph of a derivative related to a function.

Types of Problems
There is one type of problem in this exercise:


 * 1) Move the points to make the derivative: This function provides a graph with several orange points. The student is expected to move the orange points to the correct values on the grid to make the derivative.Derint1.png

Strategies
Knowledge of tangent lines and graphing are encouraged to ensure success on this exercise.
 * 1) The tangent line hits the curve at a single point and is the limit of secant lines about the point.
 * 2) This problem will draw the graph of the derivative when the points are moved correctly. It is not possible to get this problem wrong as long as patience is practiced.

Real-life Applications

 * 1) Calculus has massive applications to physics, chemistry, biology, economics and many other fields.
 * 2) The slope of a curve is the natural extension of a linear slope.