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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a critical point.
💡 Hint: Think about what the first derivative indicates about the function.
Question 2
Easy
What is the first derivative test used for?
💡 Hint: Consider how the function behaves before and after the critical point.
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 do critical points signify in a function?
- They are always maximum points
- They are where the first derivative is zero or undefined
- They represent endpoints of the domain
💡 Hint: Think about what information the first derivative provides.
Question 2
True or False: A local minimum is a point that is lower than all points in the domain.
- True
- False
💡 Hint: Reflect on the definition of local minima.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer wants to create a rectangular fence for a section of land using 200 meters of fencing. How should the dimensions be chosen to maximize the area? Provide a detailed solution.
💡 Hint: Ensure to express area in terms of one variable and differentiate.
Question 2
Given the function f(x) = 4x - x², find the maximum value and its corresponding x-coordinate. Provide detailed workings.
💡 Hint: Perform the first derivative test to locate the maximum.
Challenge and get performance evaluation