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This lesson covers finding stationary points, classifying them, identifying points of inflection, and developing a systematic approach to curve sketching. These are essential skills for A-Level Mathematics and are examined in both pure and applied contexts.
A stationary point occurs where the gradient of a curve is zero:
dy/dx = 0
At a stationary point, the tangent to the curve is horizontal.
Examine the sign of dy/dx on either side of the stationary point:
| Sign change of dy/dx | Type |
|---|---|
| + → 0 → − | Local maximum |
| − → 0 → + | Local minimum |
| + → 0 → + | Rising point of inflection |
| − → 0 → − | Falling point of inflection |
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