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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Identify if the function f(x) = 2x + 3 is increasing or decreasing.
💡 Hint: Check the derivative.
Question 2
Easy
What is the derivative of f(x) = 3x^2 + 5?
💡 Hint: Differentiate using power rules.
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 it mean for a function to be increasing?
- a) The outputs decrease as inputs increase
- b) The outputs increase as inputs increase
- c) There is no change in output
- d) The function is constant
💡 Hint: Think about the definition of increasing functions.
Question 2
True or False: A local minimum occurs when the first derivative changes from negative to positive.
- True
- False
💡 Hint: Recall the first derivative test.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A farmer has a rectangular piece of land with a fixed perimeter of 100 meters. Determine the dimensions that maximize the area of the field.
💡 Hint: Express width in terms of length and apply the area formula.
Question 2
Given the function f(x) = -3x^2 + 4x + 5, find the coordinates of the vertex and determine if it is a maximum or minimum.
💡 Hint: Use the vertex formula x = -b/(2a) for the maximum point of a parabola.
Challenge and get performance evaluation