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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define what it means for a function to be increasing.
💡 Hint: Think about the movement of the graph as you move from left to right.
Question 2
Easy
How can you determine if a function is decreasing using derivatives?
💡 Hint: Remember 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 indicates that a function is increasing on an interval?
- f′(x) < 0
- f′(x) = 0
- f′(x) > 0
💡 Hint: Consider the definition.
Question 2
True or False: If a function is decreasing, then f′(x) > 0 for all x in that interval.
- True
- False
💡 Hint: Think of the graph slope.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
For f(x) = 2x³ - 4x² + 1, find intervals of increase and decrease and justify your answer.
💡 Hint: Examine the signs of the derivative!
Question 2
Show that the function f(x) = -x³ + 3x² - 2 has a local maximum at a specific point.
💡 Hint: Look for sign changes in the first derivative.
Challenge and get performance evaluation