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.
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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
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) = 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
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) = x³ − 6x² + 9x, the gradient function is f'(x) = 3x² − 12x + 9. Find the intervals where f is increasing.
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