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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the critical points for f(x) = x^2 - 4x + 4.
💡 Hint: Set the first derivative f'(x) equal to zero.
Question 2
Easy
What does it mean if f''(c) > 0?
💡 Hint: Think about concavity.
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 local maximum in the Second Derivative Test?
- f''(x) > 0
- f''(x) < 0
- f''(x) = 0
💡 Hint: Think about how concavity relates to maxima.
Question 2
True or False: The Second Derivative Test can always definitively classify critical points.
- True
- False
💡 Hint: Consider scenarios when the second derivative doesn't provide clarity.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = x^4 - 4x^3 + 4x, find and classify all of its critical points.
💡 Hint: Calculate the first and second derivatives.
Question 2
Using the function f(x) = x^3 - 9x + 7, determine if there exist any points of inflection.
💡 Hint: After calculating the second derivative, remember to check signs in the intervals.
Challenge and get performance evaluation