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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the average rate of change of \( f(x) = 3x^2 - 2x \) from \( x = 1 \) to \( x = 4 \)?
💡 Hint: Use the formula \\( \\frac{f(4) - f(1)}{4 - 1} \\).
Question 2
Easy
Find the instantaneous rate of change of \( s(t) = 4t^2 - t + 1 \) at \( t = 2 \).
💡 Hint: Calculate the derivative and evaluate it at \\( t = 2 \\).
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: Think about the change in the function divided by the change in the interval.
Question 2
True or False: The instantaneous rate of change is the derivative of the function.
- True
- False
💡 Hint: Consider how we define the derivative mathematically.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A car's position over time is given by \( s(t) = 5t^3 - 4t^2 + 2t \). What is the average rate of change from \( t = 1 \) to \( t = 3 \)?
💡 Hint: Evaluate the function at both time points!
Question 2
Given the function \( f(x) = e^x \), find the instantaneous rate of change at \( x = 0 \).
💡 Hint: What is the derivative of the exponential function?
Challenge and get performance evaluation