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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify whether f(x) = 2x + 3 is increasing or decreasing.
💡 Hint: Check the sign of the derivative.
Question 2
Easy
What is the local maximum for f(x) = x^2 - 4?
💡 Hint: Set the derivative to zero.
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
When is a function considered increasing?
- When its derivative is negative
- When its derivative is positive
- When its derivative is zero
💡 Hint: Think about the behavior of the function.
Question 2
A local minimum occurs at a point where the derivative changes from increasing to decreasing.
- True
- False
💡 Hint: Consider the direction of the curve.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function f(x) = 2x^3 - 12x^2 + 18x, find the local maximum and minimum values.
💡 Hint: Derivatives can reveal peaks and valleys.
Question 2
For a cone with radius r and height h, express volume V as a function of r and find the rate of change when r is changing.
💡 Hint: Remember to utilize related rates.
Challenge and get performance evaluation