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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the derivative in your own words.
💡 Hint: Think about what it means for a curve to be steep.
Question 2
Easy
What is the mathematical notation for a derivative?
💡 Hint: Consider what symbols represent rates of change.
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 does the derivative represent?
- Total change
- Instantaneous rate of change
- Average rate of change
💡 Hint: Think about what happens to a function at a single point.
Question 2
True or False: The derivative can be negative.
- True
- False
💡 Hint: Consider how slopes work on a graph.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the function f(x) = e^x. Use the limit definition to show that f'(0) = 1.
💡 Hint: Use Taylor expansion or L'Hôpital's rule for simplification.
Question 2
Prove that the derivative of f(x) = ln(x) at x = 1 is 1.
💡 Hint: Recall properties of logarithms and their behavior near 1.
Challenge and get performance evaluation