Graphs of functions and their derivatives

The  exercise appears under the Differential calculus Math Mission. This exercise tries to foster a connection between the derivative and the function through their graphs.

Types of Problems
There are three types of problems in this exercise:


 * 1) Find the connection between the function and it's derivative: This problem has function and it's derivative. The student is asked to correctly determine the relationships between the functions and their derivatives.Gofatd1.png
 * 2) Which function is f and f'  This problem provides the graph with multiple graphs. The student is asked to determine which is the function and which is the derivative.Gofatd2.png
 * 3) Find the picture of the derivative: This problem provides a function. The student is asked to figure out which is the derivative.Gofatd3.png

Strategies
Knowledge of the graphs of functions, their derivatives, and their antiderivatives are encouraged to ensure success on this exercise.
 * 1) A derivative is positive when a function is increasing, and a function is negative when the function is decreasing.

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.