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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an increasing function.
💡 Hint: Think about the relationship between x and f(x).
Question 2
Easy
What does f'(x) > 0 indicate?
💡 Hint: Consider how the output changes for greater input.
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 indicates that a function is increasing?
- f'(x) < 0
- f'(x) = 0
- f'(x) > 0
💡 Hint: Think about how the derivative behaves!
Question 2
True or False: A critical point occurs where f'(x) = 0.
- True
- False
💡 Hint: Rethink how we define critical points.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = 2x^3 - 9x^2 + 12x, find the intervals of increase and decrease.
💡 Hint: Remember to check the signs of f' in each interval!
Question 2
Determine the critical points and analyze f(x) = x^4 - 4x^3.
💡 Hint: Critical points are where the derivative is zero. Look carefully at the function’s behavior around these points.
Challenge and get performance evaluation