Question 1

At a stationary point of f, which of the following is always true?

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Question 2

A stationary point has f'(x) changes from positive to negative. What type is it?

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Question 3

Find the stationary point of f(x) = x² − 4x + 7 and determine its nature.

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Question 4

Where is the y-coordinate of the stationary point of f(x) = 2x² − 8x + 3?

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Question 5

Find the coordinates of the stationary point of f(x) = −x² + 6x − 8 and state its nature.

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Question 6

f(x) = x² + 4x − 12. Find the minimum value of f.

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Question 7

The height of a ball is h(t) = −5t² + 20t + 2 metres. Find the maximum height.

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Question 8

f(x) = x³. Which statement about x = 0 is correct?

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Question 9

p(x) = x³ − 3x. Find the local maximum and local minimum values.

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Question 10

A function f has f'(x) = 3x² − 6x.

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Question 11

Explain how a sign diagram of f'(x) can classify a stationary point. Give an example.

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Question 12

Find and classify all stationary points of g(x) = 2x³ − 9x² + 12x − 4.

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Question 13

g(x) = x⁴ − 4x². Find all stationary points and classify them.

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Question 14

f(x) = ax³ + bx² has a stationary point at (2, 4). Find a and b.

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Question 15

A curve has equation y = x³ − 6x² + 9x + 1.

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Topic 5.6: Area Under a Curve Questions

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