1.1.5. Applications of Finite Differences

Try these first

1. 1.

   What is a finite difference?

   Hint

   Think about how derivatives are represented.

2. 2.

   Name one application of finite differences.

   Hint

   Consider how we estimate values between known points.

3. 3.

   What does a finite difference represent?

   • Change in function value
   • A geometric concept
   • An algebraic identity

   Hint

   Think back to the definition of finite differences.

4. 4.

   True or False: Finite differences are only used for interpolation.

   • True
   • False

   Hint

   Consider the multiple uses of finite differences.

5. 5.

   Given the function values f(1)=3, f(2)=6, f(3)=11, calculate the first and second forward differences.

   Hint

   Use the finite difference formula for each step.

6. 6.

   How would you apply finite differences to approximate the derivative of f(x)=x^2 at x=2?

   Hint

   Compute f(2+h) and subtract f(2).