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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the first derivative of the function f(x) = 3x² - 5x + 2.
💡 Hint: Differentiate each term of the polynomial.
Question 2
Easy
Identify a critical point for the function f(x) = x² + 4.
💡 Hint: Calculate the derivative and check for zeros.
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 is a critical point?
- Where f'(x) is zero
- Where f(x) is maximum
- Both A and B
💡 Hint: Focus on the definition of critical points.
Question 2
True or False: A critical point can be a minimum even if it doesn't satisfy f'(x) = 0.
- True
- False
💡 Hint: Consider cases where the derivative might not be defined.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A company models its profit as P(x) = -x³ + 9x² - 24x. Find the critical points and classify them.
💡 Hint: Use the first derivative test for classification.
Question 2
Find the local extrema for the function f(x) = x⁴ - 4x³ + 4x. Determine not only the points but also the function's behavior.
💡 Hint: Graphing the function could provide visual insight into its behavior.
Challenge and get performance evaluation