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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the critical points of f(x) = 2x^2 - 4x + 1.
💡 Hint: Consider where the derivative changes signs.
Question 2
Easy
Is f(x) = x^2 increasing or decreasing at x = 1?
💡 Hint: Check the derivative value at that point.
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 the First Derivative Test help to determine?
- Where a function is constant
- Local maxima and minima
- Inflection points
💡 Hint: Remember the test focuses on the behavior around critical points.
Question 2
True or False: If the derivative at a critical point is positive, the function has a local minimum.
- True
- False
💡 Hint: Consider what it means for a function to be increasing or decreasing.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find all critical points of f(x) = sin(x) on the interval [0, 2π] and classify them.
💡 Hint: The derivative of sin(x) is cos(x); set it to zero for critical points.
Question 2
A farmer wants to enclose a rectangular field with a fixed perimeter of 100m. What dimensions will maximize the area?
💡 Hint: Use the area formula and derivative to find critical points.
Challenge and get performance evaluation