1.1.2. Types of Finite Differences

Try these first

1. 1.

   What is the formula for the forward difference?

   Hint

   Think about how we define changes in functions.

2. 2.

   Define backward difference.

   Hint

   Consider how we look at the previous function value.

3. 3.

   What does the forward difference calculate?

   • Change at a point
   • Average of two points
   • Change from past value

   Hint

   Remember the definition of forward difference.

4. 4.

   Is the center difference method always more accurate than forward and backward methods?

   • True
   • False

   Hint

   Think about accuracy in approximations.

5. 5.

   Given a set of function values for f(x): f(1) = 2, f(2) = 5, f(3) = 10, construct a difference table and find the second differences. Use this to predict f(4).

   Hint

   Start by calculating the first differences, then proceed to the second.

6. 6.

   Create a real-life scenario where finite differences could play a role in predicting outcomes. Analyze the impacts based on different incremental values.

   Hint

   Look for patterns when calculating with different years.