6.2 - Examples
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Practice Questions
Test your understanding with targeted questions
Determine if f(x) = 2x + 3 is increasing or decreasing.
💡 Hint: Check the sign of the derivative.
Find the first derivative of f(x) = 4x² - 5.
💡 Hint: Apply the power rule for derivatives.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is true about increasing functions?
💡 Hint: Remember the definition of increasing functions.
True or False: The local maximum occurs where the first derivative changes from positive to negative.
💡 Hint: Think about how the slope behaves at maximum points.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
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