1.1.7. Example Problems

Try these first

1. 1.

   Define a finite difference.

   Hint

   Think about how we determine changes in function values.

2. 2.

   What is the formula for the first forward difference?

   Hint

   Remember how you calculate the change in function value.

3. 3.

   What is the first forward difference for f(1) if f(1)=1 and f(2)=8?

   • 7
   • 6
   • 5

   Hint

   Look at the values of f at points 1 and 2.

4. 4.

   True or False: The second forward difference is calculated from the first forward differences.

   • True
   • False

   Hint

   Recall how the terms relate to each other.

5. 5.

   Calculate the first and second forward differences for the function defined at points x = 2, 4, 6, 8 with values 3, 12, 27, 48.

   Hint

   Use the same forward difference formulas.

6. 6.

   Explain the significance of finite differences in the derivation of numerical differentiation techniques.

   Hint

   Make connections between finite differences and slope calculations!