Unit 5: Calculus
Topic 5.7: The Second Derivative Questions
Practice 8 exam-style questions for IB Math AA SL Topic 5.7. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1State2 marks
2026• Aimnova practice — 5.7.1
A curve has a stationary point at x = 2, where f''(2) = −5. State the nature of this point.
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2026• Aimnova practice — 5.7.1
Given f(x) = 2x³ − 5x + 1, find f''(x).
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2026• Aimnova practice — 5.7.1
For f(x) = x³ − 12x, find the stationary points and classify them with the second-derivative test.
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2026• Aimnova practice — 5.7.1
Given y = x⁴, find d²y/dx² and state the concavity of the curve for x > 0.
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2026• Aimnova practice — 5.7.1
For f(x) = 2x³ − 9x² + 12x, find the x-coordinate where the concavity changes.
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2026• Aimnova practice — 5.7.1
A curve has f'(x) = 3x² − 6x. Find f''(x), and use it to classify the stationary point at x = 2.
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2026• Aimnova practice — 5.7.1
For f(x) = x³ − 6x², find the values of x for which the curve is concave up.
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2026• Aimnova practice — 5.7.1
A curve has a stationary point at x = −1 where f''(−1) = 0. Explain why the second-derivative test cannot classify it.
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