Unit 5: Calculus
Topic 5.2: Increasing and Decreasing Functions Questions
Practice 8 exam-style questions for IB Math AA SL Topic 5.2. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Determine2 marks
2026• Aimnova practice — 5.2.1
A function has f'(x) = 12 − 3x. Determine whether f is increasing or decreasing at x = 5.
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2026• Aimnova practice — 5.2.1
For f(x) = x² − 10x + 3, the gradient function is f'(x) = 2x − 10. Find the values of x for which f is increasing.
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2026• Aimnova practice — 5.2.1
The graph of f' crosses the x-axis at x = −3 (going − to +) and at x = 1 (going + to −). State the nature of f at each x-value.
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2026• Aimnova practice — 5.2.1
For f(x) = 2x² − 12x + 7, find the value of x at which f stops decreasing and starts increasing.
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2026• Aimnova practice — 5.2.1
Show that f(x) = x³ + 2x is increasing for all real x.
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2026• Aimnova practice — 5.2.1
A function f is increasing for x < 2 and decreasing for x > 2. State what happens at x = 2 and the value of f'(2).
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2026• Aimnova practice — 5.2.1
For f(x) = x³ − 12x, the gradient function is f'(x) = 3x² − 12. Find the values of x for which f is decreasing.
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2026• Aimnova practice — 5.2.1
For f(x) = x³ − 6x² + 9x, the gradient function is f'(x) = 3x² − 12x + 9. Find the intervals where f is increasing.
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