Practice - Example 2
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Practice Questions
Test your understanding with targeted questions
Define a critical point.
💡 Hint: Think about what the first derivative indicates about the function.
What is the first derivative test used for?
💡 Hint: Consider how the function behaves before and after the critical point.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What do critical points signify in a function?
💡 Hint: Think about what information the first derivative provides.
True or False: A local minimum is a point that is lower than all points in the domain.
💡 Hint: Reflect on the definition of local minima.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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