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Flip to reveal answersWhen is a function increasing?
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All 9 Flashcards — Increasing & decreasing
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Question
When is a function increasing?
Answer
Where its gradient is positive: f'(x) > 0.
Question
When is a function decreasing?
Answer
Where its gradient is negative: f'(x) < 0.
Question
How do you find where a function is increasing?
Answer
Differentiate, then solve the inequality f'(x) > 0.
Question
What separates the increasing and decreasing parts?
Answer
The stationary points, where f'(x) = 0.
Question
After finding stationary points, how do you classify the intervals?
Answer
Test the sign of f'(x) in each interval between them.
Question
On a graph of f', where is f increasing?
Answer
Where f' is above the x-axis (positive).
Question
How does the graph of f' show a local maximum of f?
Answer
f' crosses zero from positive to negative (+ → −).
Question
How does the graph of f' show a local minimum of f?
Answer
f' crosses zero from negative to positive (− → +).
Question
Do you need the size of f'(x) to test increasing/decreasing?
Answer
No — only its sign (positive or negative).
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Full study notes for Increasing & decreasing
Topic 5.2 hub
Increasing & decreasing
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