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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's slope equals zero.
Question 2
Easy
Explain the purpose of the first derivative test.
💡 Hint: Consider how the sign of the derivative 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 is a critical point?
- A point where f'(x) is zero
- A point where f'(x) is positive
- A point where f(x) increases
💡 Hint: Remember the definition of critical points.
Question 2
In the first derivative test, what indicates a local minimum?
- f'(x) > 0
- f'(x) < 0
- f'(x) changes from negative to positive
💡 Hint: Think about how the slope changes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the local maxima or minima of the function f(x) = x^3 - 6x^2 + 9x + 1.
💡 Hint: Use the second derivative to confirm.
Question 2
A farmer has 100 meters of fencing to create a rectangular enclosure. What dimensions will maximize the area?
💡 Hint: Remember the perimeter constraint P = 2l + 2w.
Challenge and get performance evaluation