Unit 5: Calculus
Topic 5.3: Increasing, Decreasing and Stationary Points Questions
Practice 20 exam-style questions for IB Math AI SL Topic 5.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find1 mark
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What is the derivative of 8x⁵?
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A function's graph is falling steeply at x = −2. Which is correct?
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Find f′(x) for f(x) = 4x³ − 3x + 7.
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Find dy/dx for y = 3x⁴ − 5x² + 2x − 8.
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The graph of g(x) rises from x = 0 to x = 5, then falls for x > 5.
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What is d/dx[−9]?
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The function f(x) = x³ − 2x. Which statement about f′(x) is correct?
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The graph of f(x) has a local minimum at x = 4. What must be true?
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The graph of f(x) has f(2) = 7 and f′(2) = −3. Describe what the curve looks like at x = 2.
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For g(x) = x³ − 12x, find the x-values where g′(x) = 0.
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For which value of x is f′(x) = 0 certain to be true?
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P(t) is the profit (thousands of dollars) after t years. P′(3) = 4. What does this mean?
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Find the gradient of f(x) = 2x³ − 6x at x = −1.
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Expand and then differentiate y = (x + 2)(x − 3).
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T(x) is the temperature (°C) of a reaction at time x (minutes). The graph of T(x) is a smooth curve that peaks at x = 8. State two things that can be concluded about T′(8).
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h(x) = −x³ + 6x².
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The graph of a function passes through A(1, 4) and B(3, 4) with a smooth peak between them. A student says: "f′(1) = f′(3) because the function has the same y-value at both points." Is the student correct? Explain using the meaning of f′.
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A car's position (metres) at time t (seconds) is s(t) = t² + 2t.
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State the difference between f(a) and f′(a). Give a real-world example of a function and explain what both values represent in that context.
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h(t) = −5t² + 20t is the height (metres) of a ball at time t (seconds). Without calculating, state what h′(t) = 0 tells you about the motion of the ball.
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