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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 comparing values of the function.
Question 2
Easy
What does it mean for a function to be decreasing?
💡 Hint: Look at how the function's value changes.
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 denotes a function as increasing?
- f'(x) < 0
- f'(x) > 0
- f'(x) = 0
💡 Hint: Think about how derivative signs affect function behavior.
Question 2
True or False: A local maximum occurs where the derivative changes from negative to positive.
- True
- False
💡 Hint: Visualize how the function behavior changes at those points.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
You have a rectangular garden that must have a total perimeter of 100 meters. What dimensions yield the maximum area?
💡 Hint: Use the perimeter equation to express area as a function of one variable.
Question 2
Analyze f(x) = -x^4 + 4x^2. Find the local extrema and classify them.
💡 Hint: Use first and second derivative tests to classify all critical points.
Challenge and get performance evaluation