Practice Key Takeaways (8) - Maxima and Minima - IB 10 Mathematics

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6 sample questions

Question 1.
What is a critical point?
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Think about where the function's slope equals zero.
Question 2.
Explain the purpose of the first derivative test.
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Consider how the sign of the derivative changes.
3Question 3.
What is a critical point?
- A point where f'(x) is zero
- A point where f'(x) is positive
- A point where f(x) increases
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Remember the definition of critical points.
4Question 4.
In the first derivative test, what indicates a local minimum?
- f'(x) > 0
- f'(x) < 0
- f'(x) changes from negative to positive
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Think about how the slope changes.
Question 5.
Find the local maxima or minima of the function f(x) = x^3 - 6x^2 + 9x + 1.
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Use the second derivative to confirm.
Question 6.
A farmer has 100 meters of fencing to create a rectangular enclosure. What dimensions will maximize the area?
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Remember the perimeter constraint P = 2l + 2w.

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