alleryStart learning →What does the sign of f ′(x) tell you?
Exercise and reference answers
- Items
- Item
- f ′(x) > 0 throughout
- Category
- Increasing
- Item
- x₁ < x₂ gives f(x₁) < f(x₂)
- Category
- Increasing
- Item
- f ′(x) < 0 throughout
- Category
- Decreasing
- Item
- x₁ < x₂ gives f(x₁) > f(x₂)
- Category
- Decreasing
- Item
- f(x) = c for all x
- Category
- Constant
- Item
- f ′(x) = 0 throughout the interval
- Category
- Constant
- Categories
- Item
- Increasing
- Item
- Decreasing
- Item
- Constant
Explanation
Your syllabus gives f ′(x) ≥ 0 on an interval as the test for increasing and f ′(x) ≤ 0 for decreasing.
Everything else in the chapter builds on reading that sign.
Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
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