Practice Second Derivative Test (3.1) - Maxima and Minima - IB 10 Mathematics – Group 5, Calculus

Practice: Second Derivative Test

Lesson 3.1Maxima and Minima

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10 questions

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6 sample questions

Question 1.
What is a critical point?
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Think about the definition of the first derivative.
Question 2.
What does f''(c) > 0 indicate?
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Consider concavity to determine if it is a minimum or maximum.
3Question 3.
What is the main purpose of the Second Derivative Test?
- To find critical points
- To classify critical points
- To find the first derivative
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Recall what we check with the second derivative.
4Question 4.
If f''(c) = 0, what does it imply?
- True
- False
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Think about when the second derivative test doesn't provide a definitive result.
Question 5.
Using the function f(x) = -x^4 + 4x^3, find all critical points, classify them with the second derivative test, and identify the points of inflection.
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Solve for critical points using the first derivative and analyze points using the second derivative.
Question 6.
An optimization problem states: You need to build a rectangular field with a fixed perimeter of 40m. What dimensions maximize the area?
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You need to set up the area equation, find its derivative, and apply the second derivative test.

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