Linearization

Math

Definition

The process of approximating a function near a specific point using the tangent line at that point. The linear approximation L(x) = f(a) + f'(a)(x − a) gives a good estimate for f(x) when x is close to a.

Examples

  • Approximating √4.1 using the tangent line to f(x) = √x at x = 4
  • Estimating sin(0.1) ≈ 0.1 using linearization at x = 0
  • Approximating (1.02)⁵ using the tangent line to f(x) = x⁵ at x = 1
Key Fact

L(x) = f(a) + f'(a)(x − a)

Related Terms

Tangent lines Derivative definition Implicit differentiation

Study This Concept

Practice linearization with free review games in these units:

AP Calculus AB Unit 4: Contextual Applications of Differentiation