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