Practice First Derivative Test (2.1) - Maxima and Minima - IB 10 Mathematics – Group 5, Calculus

Practice: First Derivative Test

Lesson 2.1Maxima and Minima

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10 questions

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6 sample questions

Question 1.
Identify the critical points of f(x) = x^3 - 3x^2 + 4.
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Start by calculating the first derivative.
Question 2.
What does it mean if the first derivative does not change sign at a critical point?
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Think about what happens when the function continues to increase or decrease.
3Question 3.
What is the First Derivative Test used for?
- To find second derivatives
- To classify critical points
- To determine intervals of increase only
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Consider what the name implies about its function.
4Question 4.
If f'(x) changes from positive to negative at x = c, what can we conclude?
- True
- False
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A peak point generally implies a change in direction.
Question 5.
Consider the function f(x) = x^4 - 8x^3 + 18x^2. Use the First Derivative Test to identify critical points and classify them.
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Be careful to check signs on either side of your critical points!
Question 6.
Create a real-world problem involving optimization—design a garden that maximizes area given a fixed perimeter. Formulate it and solve using derivatives.
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Sketching or visualizing the scenario can help solidify how we use these concepts in practice.

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