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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the derivative of f(x) = x²?
💡 Hint: Differentiate using the power rule.
Question 2
Easy
Is f(x) = -x² increasing or decreasing?
💡 Hint: Check the sign of the derivative.
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 does it mean if f'(x) > 0?
- The function is increasing
- The function is decreasing
- Cannot determine
💡 Hint: Think about how the function behaves as its input grows.
Question 2
Is local minima found where the first derivative is zero and f''(x) > 0?
- True
- False
💡 Hint: Remember the role of the second derivative test.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation