Unit 5: Calculus
Topic 5.8: Stationary Points and Optimisation Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.8. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026
A number x and a second number sum to 20. Their product is . Find the maximum product.
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2026
Write down the -values of the stationary points.
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2026
Write down the minimum cost of the journey.
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2025
A closed cylinder has radius cm, height cm and volume cm3. Show that its total surface area is .
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2026
Find the coordinates of the minimum point of f(x) = 2x2 − 8x + 1.
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2025
A function f has second derivative f″(x) = 6x − 12, so f″(2) = 0.
State, with a reason, whether there is a point of inflexion on the graph of y = f(x) at x = 2.
State, with a reason, whether there is a point of inflexion on the graph of y = f(x) at x = 2.
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2025
An open box has volume cm3, for . Write down the value of when .
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2026
Consider , where .
Show that the solutions to the equation are .
Show that the solutions to the equation are .
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2026
Write down the -value of the possible point of inflexion.
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2021
A function has derivative . State the three values of at which .
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2025
The function f has derivative f′(x) = 3x2 − 12, and f′(2) = 0.
State, with a reason, whether f has a local maximum or a local minimum at x = 2.
State, with a reason, whether f has a local maximum or a local minimum at x = 2.
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2026
Find the coordinates of the stationary point of f(x) = x2 − 6x + 5, and state its nature.
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2026
Find the coordinates of the minimum point of .
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2026
Find the x-coordinate of the point of inflexion of f(x) = x3 − 9x2 + 7x.
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2025
The derivative of a function f is f′(x) = x2 − 3x − 4. The graph of y = f(x) has a horizontal tangent at x = −1.
State, with a reason, whether f has a local maximum or a local minimum at x = −1.
State, with a reason, whether f has a local maximum or a local minimum at x = −1.
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2022
The graph of is a translation of . Write down where its point of inflexion is.
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2025
Show that can be written as .
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2026
A GDC graph of the surface area shows that its minimum value, cm2, occurs when cm. Write down the radius that gives the minimum surface area.
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2026
A number x and a second number sum to 20. Their product is P = x(20 − x). Find the maximum product.
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2026
Find the x-coordinate of the point of inflexion of .
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