AI reviewed · sources pending. Book associations have not been verified.
Local linear approximation
ConceptA smooth curve can often be approximated by its tangent line near a chosen point.
Explanation or usage
The tangent line at a point matches the curve’s value and slope there. For a differentiable curve, it can approximate the curve near that point; how accurate it is depends on the neighborhood and the curve’s behavior. A good local approximation need not describe a large interval well.
Common misunderstandings
A tangent line that works nearby must be correct everywhere.
In How Not to Be Wrong
General context reviewed · book attribution and sources pending
This concept can help distinguish nearby straight-line approximations from globally curved relationships.