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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) = x² + 4 is increasing or decreasing.
💡 Hint: Consider the value of 2x for any x.
Question 2
Easy
Determine the critical points for the function f(x) = -x² + 6x.
💡 Hint: Find the first derivative and set it 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
What indicates that a function is increasing over an interval?
- f'(x) < 0
- f'(x) = 0
- f'(x) > 0
💡 Hint: Think about the sign of the derivative.
Question 2
True or False: A function can have both local maxima and local minima.
- True
- False
💡 Hint: Consider examples of different function shapes.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A business finds its profit function is represented by P(x) = -x² + 10x. Determine the number of units x that maximizes profit.
💡 Hint: Find the vertex of the quadratic function.
Question 2
Explore how the optimization problem changes if the perimeter of a rectangle is increased to 30m. What dimensions yield the maximum area?
💡 Hint: Use the perimeter equation to set up the area equation.
Challenge and get performance evaluation