1.2 - Chapter Content
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Practice Questions
Test your understanding with targeted questions
What is the derivative of f(x) = x²?
💡 Hint: Differentiate using the power rule.
Is f(x) = -x² increasing or decreasing?
💡 Hint: Check the sign of the derivative.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean if f'(x) > 0?
💡 Hint: Think about how the function behaves as its input grows.
Is local minima found where the first derivative is zero and f''(x) > 0?
💡 Hint: Remember the role of the second derivative test.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Determine the maximum profit for a company given the profit function P(x) = -5x² + 100x, and find when it occurs.
💡 Hint: Differentiate P(x) and set equal to zero.
A container is to be made with a square base and open top. The surface area is fixed at 100 m². Find the dimensions of the box that maximize the volume.
💡 Hint: Express height in terms of base side length and surface area.
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