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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the area function for a rectangle with a perimeter of 20 cm?
💡 Hint: Express the area in terms of one variable.
Question 2
Easy
What is the first derivative of A(x) = 10x - x²?
💡 Hint: Differentiate the area function.
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 is the first step in solving an optimization problem?
- Set the area function
- Identify the perimeter
- Find the length and width
💡 Hint: Remember the formula for area.
Question 2
True or False: Critical points occur where the first derivative is zero.
- True
- False
💡 Hint: Recall the definition of critical points.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer has 100 meters of fencing to create a rectangular enclosure. How can they optimize the area? What dimensions will maximize the area?
💡 Hint: Use the same methods as we practiced; don’t forget to relate perimeter to length and width.
Question 2
You want to design a rectangular billboard with a fixed perimeter of 90 meters to maximize visible area. What dimensions will you choose?
💡 Hint: Remember to express the area in terms of a single variable.
Challenge and get performance evaluation