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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define an increasing function.
💡 Hint: Think about how the function behaves as x increases.
Question 2
Easy
What does it mean for a function to be decreasing?
💡 Hint: Imagine the slope of the function.
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
A function is increasing on an interval if:
- f'(x) > 0
- f'(x) < 0
- f'(x) = 0
💡 Hint: Think about the direction of the graph.
Question 2
Maxima occur where:
- True
- False
💡 Hint: Consider the first derivative test.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer wants to fence a rectangular area of 500 m² using only 200 m of fencing. What dimensions will maximize the area?
💡 Hint: Set up an equation with area and perimeter constraints.
Question 2
For the function f(x) = x^4 - 12x^2 + 36, determine the global maximum and minimum on [-3, 3].
💡 Hint: Check both endpoints and critical points around the interval.
Challenge and get performance evaluation