3.6 - Worked Example
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Practice Questions
Test your understanding with targeted questions
What does h represent in the context of finding a derivative using the central difference formula?
💡 Hint: Think about how we calculate the difference between points.
Given f(2) = 4 and f(2.2) = 5, what is the approximate value of f'(2)?
💡 Hint: Use the central difference formula.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the central difference formula used for?
💡 Hint: Recall its definition from our discussions.
True or False: The step size (h) affects the accuracy of numerical differentiation.
💡 Hint: Think about the implications of our previous example.
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Challenge Problems
Push your limits with advanced challenges
Consider a function given by the points x = [0, 1, 2, 3] and f(x) = [0, 1, 4, 9]. Use numerical differentiation to calculate the approximate value of f'(2). What do the results tell you about the behavior of the function?
💡 Hint: Consider the average slope between the points to determine the derivative at x = 2.
Evaluate the error in your numerical differentiation for the given function values. If h = 0.5 and you find f'(2) using central difference, how would you verify the accuracy?
💡 Hint: Remember to analyze the difference between the calculated derivative and the true derivative.
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