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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a critical point?
💡 Hint: Think about where the slope of the tangent line is zero.
Question 2
Easy
Define local maxima and minima in your own words.
💡 Hint: Consider how hills and valleys look on a graph.
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 a critical point?
- Where f'(x) > 0
- Where f'(x) = 0 or is undefined
- Where f''(x) = 0
💡 Hint: Think about where the slope of the function changes.
Question 2
True or False: A local minimum occurs when the first derivative changes from negative to positive.
- True
- False
💡 Hint: Consider the sound of a valley on a graph.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer wants to fence a rectangular area of 200 m². Determine the dimensions that would minimize the fencing needed.
💡 Hint: Set area = length * width and use the perimeter formula to create equations.
Question 2
A box with a square base and an open top must have a volume of 500 cm³. Find the dimensions that minimize the material needed.
💡 Hint: Use volume constraints to express the height in terms of base area and apply derivatives.
Challenge and get performance evaluation