Slope of secant lines

The  exercise appears under the Differential calculus Math Mission. This exercise plays with the formula for average rate of change to better understand the pre-derivative.

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


 * 1) Find the interval for the AROC: This problem provides a function and the slope of a particular secant line. The student is asked to select the interval that is appropriate for the given expression.Sosl1.png
 * 2) Compare the expressions: This problem provides several secant line slope expressions with a diagram. The student is asked to select the correct comparison symbol for the different expressions.Sosl2.png

Strategies
Knowledge of average rate of change (AROC) and 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 interval endpoints can be used to find the correct representation efficiently.
 * 3) On the second problem, the geometric interpretation of slope can increase efficiency.

Real-life Applications

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