Calculus › Section D · Applications of derivatives › Topic D.9
Linear approximation and differentials
Near any point where a function is smooth, the curve behaves like its tangent line. That single observation gives you fast estimates and honest error margins without a calculator.
In this topic
- The tangent as a local stand-in
- The linearisation formula
- Worked example: a square root without a calculator
- Differentials: dy versus the real change
- Worked example: how close is close?
- Propagating measurement error
- Worked example: the measured sphere
- Over or under? Let concavity answer
- Common mistakes to avoid
- Key takeaways
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Standards: 4