Math
Linearization.
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
Real-world.
- 1 Approximating √4.1 using the tangent line to f(x) = √x at x = 4
- 2 Estimating sin(0.1) ≈ 0.1 using linearization at x = 0
- 3 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)