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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a critical point?
💡 Hint: Think about where the function changes direction.
Question 2
Easy
What does a positive second derivative indicate at a critical point?
💡 Hint: Focus on the shape of the graph.
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 do we call points where the first derivative is zero?
- Turning Points
- Local Maximum
- Critical Points
💡 Hint: Focus on what defines these special points.
Question 2
True or False: A local minimum has a positive second derivative.
- True
- False
💡 Hint: Think about the shape of the graph at the minimum.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = 3x^4 - 8x^3 + 12x^2 - 5, identify all critical points and classify them using both derivative tests.
💡 Hint: Apply both tests for a comprehensive analysis.
Question 2
A cylinder's volume is represented by V(r) = πr^2h. If the height is constant at 10 cm, find the radius that maximizes the volume.
💡 Hint: Focus on the volume expression to simplify the terms!
Challenge and get performance evaluation