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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify the critical points of \( f(x) = x^3 - 3x + 2 \).
💡 Hint: First, find the derivative \\( f'(x) \\) and set it to zero.
Question 2
Easy
True or False: Every critical point is a turning point.
💡 Hint: Recall the definitions of critical points and turning points.
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 a critical point?
- When \\( f(x) = 0 \\)
- When \\( f'(x) = 0 \\)
- When \\( f''(x) = 0 \\)
💡 Hint: Think about the definitions we've discussed.
Question 2
True or False: A local maximum occurs when the first derivative goes from positive to negative.
- True
- False
💡 Hint: Recall the First Derivative Test concept.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Determine the maximum volume of a rectangular box with a square base and an open top, given a surface area of 108 square units.
💡 Hint: Start with expressing the relationship between surface area, base area, and volume.
Question 2
Analyze the function \( f(x) = x^4 - 8x^2 + 16 \) to find its critical points and classify their nature.
💡 Hint: Use the derivative approach to calculate both first and second derivatives.
Challenge and get performance evaluation