Practice - Examples
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Practice Questions
Test your understanding with targeted questions
Find the critical points of f(x) = x^2 + 2x - 8.
💡 Hint: Differentiate the function and set the result equal to zero.
Determine if f(x) = x^2 has a local maximum or minimum.
💡 Hint: Use the second derivative test.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a critical point?
💡 Hint: Think about the definition of critical points.
T/F: A local maximum can occur at a critical point.
💡 Hint: Recall the definitions of local maxima and minima.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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Reference links
Supplementary resources to enhance your learning experience.