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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What indicates a local maximum when applying the second derivative test?
💡 Hint: Remember the signs of the second derivative.
Question 2
Easy
If f''(c) = 0, what does this imply about the critical point?
💡 Hint: Think about other tests you might need.
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 the result if the second derivative at a critical point is zero?
- True
- False
💡 Hint: Remember how you classify critical points.
Question 2
If f''(c) < 0, what can we say about f(c)?
- Local Minimum
- Local Maximum
- Neither
💡 Hint: Consider the concavity of the graph!
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^2, find the critical points and classify them using the second derivative test.
💡 Hint: Re-evaluate the behavior around x = 0 for further insights.
Question 2
Using f(x) = sin(x), identify all critical points in the interval [0, 2π] and classify them using the second derivative.
💡 Hint: Address the periods of the sine function to examine critical points effectively.
Challenge and get performance evaluation