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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a critical point?
💡 Hint: Think about where the slope of the tangent is horizontal.
Question 2
Easy
What indicates a local maximum?
💡 Hint: Remember the concept of rising and falling?
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 do we call a point where a function reaches its highest value locally?
- Local Minimum
- Local Maximum
- Critical Point
💡 Hint: Think of a hilltop versus a valley.
Question 2
At a critical point, the first derivative of a function is:
- True
- False
💡 Hint: It indicates changes in direction.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = x^4 - 8x^3 + 18x^2, find its local maxima and minima.
💡 Hint: Check changes in signs from f' around critical points.
Question 2
A farmer wants to create a rectangular pen using one side of a barn as an enclosure. If the total length of fencing available is 30m, what length and width will maximize the area?
💡 Hint: Formulate the area equation and differentiate to find critical points.
Challenge and get performance evaluation