Practice - Using the Second Derivative
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Practice Questions
Test your understanding with targeted questions
What indicates a local maximum when applying the second derivative test?
💡 Hint: Remember the signs of the second derivative.
If f''(c) = 0, what does this imply about the critical point?
💡 Hint: Think about other tests you might need.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the result if the second derivative at a critical point is zero?
💡 Hint: Remember how you classify critical points.
If f''(c) < 0, what can we say about f(c)?
💡 Hint: Consider the concavity of the graph!
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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