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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the critical points of f(x) = x^2 + 2x - 8.
💡 Hint: Differentiate the function and set the result equal to zero.
Question 2
Easy
Determine if f(x) = x^2 has a local maximum or minimum.
💡 Hint: Use the second derivative test.
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 is a critical point?
- Where the function is continuous
- Where the first derivative is zero
- Where the second derivative is zero
💡 Hint: Think about the definition of critical points.
Question 2
T/F: A local maximum can occur at a critical point.
- True
- False
💡 Hint: Recall the definitions of local maxima and minima.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A quadratic function f(x) = ax^2 + bx + c has a maximum at x = 4 and a minimum at x = -2. Find the relations between a, b, and c.
💡 Hint: Consider the properties of the quadratic function and the effects of a, b, and c on its shape.
Question 2
You are optimizing a rectangular garden's area with a fence of 60m total length. Determine the dimensions that maximize the area.
💡 Hint: Formulate the area equation based on fixed perimeter and solve using differentiation.
Challenge and get performance evaluation