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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine if f(x) = 2x + 3 is increasing or decreasing.
💡 Hint: Check the sign of the derivative.
Question 2
Easy
Find the first derivative of f(x) = 4x² - 5.
💡 Hint: Apply the power rule for derivatives.
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 true about increasing functions?
- f'(x) > 0
- f'(x) < 0
- f'(x) = 0
💡 Hint: Remember the definition of increasing functions.
Question 2
True or False: The local maximum occurs where the first derivative changes from positive to negative.
- True
- False
💡 Hint: Think about how the slope behaves at maximum points.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer wants to create a rectangular field with a fixed area of 500 m². What should be the dimensions of the field that minimize the perimeter?
💡 Hint: Express perimeter in terms of one variable and set up an optimization problem.
Question 2
Find the maximum volume of a rectangular box with a square base and open top, given a surface area of 600 m².
💡 Hint: Use surface area constraints to derive volume in a single variable and optimize.
Challenge and get performance evaluation