Practice Turning Points (1.2) - Maxima and Minima - IB 10 Mathematics – Group 5, Calculus

Practice: Turning Points

Lesson 1.2Maxima and Minima

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9 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Identify the critical points of $f(x) = x^3 - 3x + 2$ .
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First, find the derivative \$ f'(x) \$ and set it to zero.
Question 2.
True or False: Every critical point is a turning point.
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Recall the definitions of critical points and turning points.
3Question 3.
What indicates a critical point?
- When \$ f(x) = 0 \$
- When \$ f'(x) = 0 \$
- When \$ f''(x) = 0 \$
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Think about the definitions we've discussed.
4Question 4.
True or False: A local maximum occurs when the first derivative goes from positive to negative.
- True
- False
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Recall the First Derivative Test concept.
Question 5.
Determine the maximum volume of a rectangular box with a square base and an open top, given a surface area of 108 square units.
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Start with expressing the relationship between surface area, base area, and volume.
Question 6.
Analyze the function $f(x) = x^4 - 8x^2 + 16$ to find its critical points and classify their nature.
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Use the derivative approach to calculate both first and second derivatives.

5 more questions in this section. Enroll free to practise them all.