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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define local maximum and local minimum.
💡 Hint: Think about the hills and valleys in a graph.
Question 2
Easy
What is a critical point?
💡 Hint: These points are where the slope is flat or does not exist.
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 happens at a local maximum?
- The function rises
- The function is flat
- The function falls
💡 Hint: Think of hills where you walk to the top.
Question 2
True or False: A local minimum can occur if the first derivative is positive.
- True
- False
💡 Hint: Visualize how a curve behaves at its lowest point.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = x^4 - 8x^2 + 3, find the local maxima and minima and classify them using both the first and second derivative tests.
💡 Hint: Look out for changes in the sign of the derivative around your critical points.
Question 2
What is the global maximum of the function f(x) = -x^2 + 6x - 8 on the closed interval [0, 5]?
💡 Hint: Make sure to include evaluations at the boundaries!
Challenge and get performance evaluation