Practice - First Derivative Test
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Practice Questions
Test your understanding with targeted questions
Identify the critical points of f(x) = x^3 - 3x^2 + 4.
💡 Hint: Start by calculating the first derivative.
What does it mean if the first derivative does not change sign at a critical point?
💡 Hint: Think about what happens when the function continues to increase or decrease.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the First Derivative Test used for?
💡 Hint: Consider what the name implies about its function.
If f'(x) changes from positive to negative at x = c, what can we conclude?
💡 Hint: A peak point generally implies a change in direction.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Consider the function f(x) = x^4 - 8x^3 + 18x^2. Use the First Derivative Test to identify critical points and classify them.
💡 Hint: Be careful to check signs on either side of your critical points!
Create a real-world problem involving optimization—design a garden that maximizes area given a fixed perimeter. Formulate it and solve using derivatives.
💡 Hint: Sketching or visualizing the scenario can help solidify how we use these concepts in practice.
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