The formal and alternate form of the derivative

The  exercise appears under the Differential calculus Math Mission. This exercise experiments with the connection between the different forms of the derivative.

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


 * 1) Find the function and the number: This problem provides an expression that represents  derivative. The student is asked to determine which function is being used and the point where the derivative is being evaluated.Tfaafotd1.png
 * 2) Which expression is the derivative: This problem provides a function and several possible expressions which may be the derivative. The student is asked to select which of the expressions are the derivative.Tfaafotd2.png

Strategies
Knowledge of average rate of change (AROC) and multiple forms of the derivatives are encouraged to ensure success on this exercise.
 * 1) The slope of a secant line on an interval from a to b is given by (f(b)-f(a))/(b-a).
 * 2) The two forms of a derivative are the same if a=x and b=x+h.
 * 3) Concentrating on the denominator can yield the answer more efficiently.

Real-life Applications

 * 1) Calculus has massive applications to physics, chemistry, biology, economics and many other fields.