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Increasing, decreasing and stationary points
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Learn it f is increasing where f′(x) > 0 and decreasing where f′(x) < 0. Stationary points are where f′(x) = 0; check the sign of f′ (or f″) on each side to tell a maximum from a minimum.
Example: f(x) = x³ − 12x. Stationary points?
- f′(x) = 3x² − 12 = 0 → x = ±2.
- f″(x) = 6x: x = −2 is a local max, x = 2 a local min.
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