Practice - Practice Exercises (for Students)
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Practice Questions
Test your understanding with targeted questions
Find the average rate of change of f(x) = 3x^2 - 2x from x = 1 to x = 4.
💡 Hint: Use the formula (f(b) - f(a)) / (b - a).
What is the instantaneous rate of change of f(x) = 2x + 3 at x = 3?
💡 Hint: Find the derivative of the function.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the average rate of change?
💡 Hint: Think about the formula involving two points.
True or False: The instantaneous rate of change is given by a derivative.
💡 Hint: Recall how derivatives define slopes.
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Challenge Problems
Push your limits with advanced challenges
Given the function f(x) = -2x^2 + 4x + 1, determine the average rate of change from x = 0 to x = 2, and explain what this means in practical terms.
💡 Hint: Use the average rate of change formula.
For the function g(t) = t^3 - 12t + 5, find the instantaneous rate of change at t = 2 and determine its significance.
💡 Hint: Calculate g'(t) first.
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Reference links
Supplementary resources to enhance your learning experience.