1.1.6 - Newton’s Forward and Backward Interpolation Formulas
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Practice Questions
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What is the forward interpolation formula?
💡 Hint: Recall the components of the formula from our discussion.
Define finite difference.
💡 Hint: Think about how differences in values help in approximating derivatives.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the forward interpolation formula estimate?
💡 Hint: Think of how we fill in gaps in data.
True or False: The backward interpolation formula can only estimate values after the last known point.
💡 Hint: Consider what backward means in this context.
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Challenge Problems
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Given the data points (1, 1), (2, 4), (3, 9), and (4, 16), calculate f(2.5) using the forward interpolation formula.
💡 Hint: Set up your forward difference table to help track your computations.
Using the same data points, estimate f(3.5) with the backward interpolation formula. Discuss your reasoning.
💡 Hint: Remember that you are predicting backward, so focus on the point at 3.
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