Practice Newton’s Forward And Backward Interpolation Formulas (1.1.6) - Finite Differences

Practice: Newton’s Forward and Backward Interpolation Formulas

Lesson 1.1.6Finite Differences

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6 sample questions

Question 1.
What is the forward interpolation formula?
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Recall the components of the formula from our discussion.
Question 2.
Define finite difference.
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Think about how differences in values help in approximating derivatives.
3Question 3.
What does the forward interpolation formula estimate?
- Value at existing data point
- Value between data points
- Value outside the dataset
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Think of how we fill in gaps in data.
4Question 4.
True or False: The backward interpolation formula can only estimate values after the last known point.
- True
- False
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Consider what backward means in this context.
Question 5.
Given the data points (1, 1), (2, 4), (3, 9), and (4, 16), calculate f(2.5) using the forward interpolation formula.
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Set up your forward difference table to help track your computations.
Question 6.
Using the same data points, estimate f(3.5) with the backward interpolation formula. Discuss your reasoning.
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Remember that you are predicting backward, so focus on the point at 3.

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