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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does the second derivative tell us about a function?
💡 Hint: Think about how the graph curves.
Question 2
Easy
If f''(x) > 0, what can you say about the graph?
💡 Hint: Use your knowledge on what concave up looks like.
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 does the second derivative indicate about a function’s concavity?
- Concave up
- Concave down
- Either A or B based on its value
💡 Hint: Remember the relationship between the sign of f''(x) and concavity.
Question 2
True or False: Higher order derivatives can indicate points of inflection.
- True
- False
💡 Hint: Think about when the concavity of a function changes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A car's position is given by the function s(t) = t^4 - 8t^3 + 18t^2. Find the acceleration of the car and determine if the car is speeding up or slowing down at t=2.
💡 Hint: Remember to evaluate the signs of both derivatives at t=2.
Question 2
Find and classify all critical points of the function f(x) = x^4 - 4x^3. Indicate if they are local maxima, minima, or points of inflection.
💡 Hint: Evaluate both f' and f'' around the critical points.
Challenge and get performance evaluation