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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the average rate of change of f(x) = 3x^2 - 2x from x = 1 to x = 4.
💡 Hint: Calculate f(4) and f(1) first.
Question 2
Easy
What does the average rate of change represent?
💡 Hint: Think of it as the slope between two points.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for Average Rate of Change?
💡 Hint: Remember the slope concept.
Question 2
True or False: The Instantaneous Rate of Change is the slope of the tangent line.
- True
- False
💡 Hint: Think about how we derived the tangent line.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A cyclist travels along a path defined by the function h(t) = -4t^2 + 20t + 1. Calculate the average rate of change from t = 2 to t = 4, and then find the instantaneous rate of change at t = 3.
💡 Hint: Remember the formulas for AROC and IROC, and evaluate accordingly!
Question 2
A function g(x) models the profit of a company: g(x) = 5x^2 - 10x + 15. Determine the average rate of change between x = 1 and x = 5, and explain what it indicates about the company’s profit behavior.
💡 Hint: Calculate the function values first!
Challenge and get performance evaluation